Vulnerability Parameters in Neutrosophic Graphs

Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, |𝑠(𝑢)– 𝑠(𝑣)| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score...
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Gespeichert in:

Autor*in:	R.V. Jaikumar [verfasserIn] R. Sundareswaran [verfasserIn] G. Balaraman [verfasserIn] P K Kishore Kumar [verfasserIn] Said Broumi [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	score equitable sets strong score equitable sets equitable integrity strong equitable integrity

Übergeordnetes Werk:	In: Neutrosophic Sets and Systems - University of New Mexico, 2016, 48(2022), Seite 109-121
Übergeordnetes Werk:	volume:48 ; year:2022 ; pages:109-121

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.5281/zenodo.6041365

Katalog-ID:	DOAJ08691989X

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520			\|a Let = (U, V) be a Single valued Neutrosophic graph. A subset ∈ ( ) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \| ( )– ( )\| ≤ 1, , ∊ . If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E ( ) = {\| \| + ( − ): is a score equitable set in }, where ( − ) denotes the order of the largest component in − . The strong integrity of Single valued Neutrosophic graph G which is defined as S ( ) = {\| \| + ( − ): is a strong score set in }. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds.
650		4	\|a score equitable sets
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653		0	\|a Mathematics
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700	0		\|a G. Balaraman \|e verfasserin \|4 aut
700	0		\|a P K Kishore Kumar \|e verfasserin \|4 aut
700	0		\|a Said Broumi \|e verfasserin \|4 aut
773	0	8	\|i In \|t Neutrosophic Sets and Systems \|d University of New Mexico, 2016 \|g 48(2022), Seite 109-121 \|w (DE-627)1760646911 \|x 2331608X \|7 nnns
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952			\|d 48 \|j 2022 \|h 109-121

Indexfelder

author_variant	r j rj r s rs g b gb p k k k pkkk s b sb
matchkey_str	article:2331608X:2022----::unrbltprmtrinur
hierarchy_sort_str	2022
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allfields	10.5281/zenodo.6041365 doi (DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c DE-627 ger DE-627 rakwb eng QA1-939 QA75.5-76.95 R.V. Jaikumar verfasserin aut Vulnerability Parameters in Neutrosophic Graphs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science R. Sundareswaran verfasserin aut G. Balaraman verfasserin aut P K Kishore Kumar verfasserin aut Said Broumi verfasserin aut In Neutrosophic Sets and Systems University of New Mexico, 2016 48(2022), Seite 109-121 (DE-627)1760646911 2331608X nnns volume:48 year:2022 pages:109-121 https://doi.org/10.5281/zenodo.6041365 kostenfrei https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c kostenfrei http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf kostenfrei https://doaj.org/toc/2331-6055 Journal toc kostenfrei https://doaj.org/toc/2331-608X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 48 2022 109-121
spelling	10.5281/zenodo.6041365 doi (DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c DE-627 ger DE-627 rakwb eng QA1-939 QA75.5-76.95 R.V. Jaikumar verfasserin aut Vulnerability Parameters in Neutrosophic Graphs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science R. Sundareswaran verfasserin aut G. Balaraman verfasserin aut P K Kishore Kumar verfasserin aut Said Broumi verfasserin aut In Neutrosophic Sets and Systems University of New Mexico, 2016 48(2022), Seite 109-121 (DE-627)1760646911 2331608X nnns volume:48 year:2022 pages:109-121 https://doi.org/10.5281/zenodo.6041365 kostenfrei https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c kostenfrei http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf kostenfrei https://doaj.org/toc/2331-6055 Journal toc kostenfrei https://doaj.org/toc/2331-608X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 48 2022 109-121
allfields_unstemmed	10.5281/zenodo.6041365 doi (DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c DE-627 ger DE-627 rakwb eng QA1-939 QA75.5-76.95 R.V. Jaikumar verfasserin aut Vulnerability Parameters in Neutrosophic Graphs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science R. Sundareswaran verfasserin aut G. Balaraman verfasserin aut P K Kishore Kumar verfasserin aut Said Broumi verfasserin aut In Neutrosophic Sets and Systems University of New Mexico, 2016 48(2022), Seite 109-121 (DE-627)1760646911 2331608X nnns volume:48 year:2022 pages:109-121 https://doi.org/10.5281/zenodo.6041365 kostenfrei https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c kostenfrei http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf kostenfrei https://doaj.org/toc/2331-6055 Journal toc kostenfrei https://doaj.org/toc/2331-608X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 48 2022 109-121
allfieldsGer	10.5281/zenodo.6041365 doi (DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c DE-627 ger DE-627 rakwb eng QA1-939 QA75.5-76.95 R.V. Jaikumar verfasserin aut Vulnerability Parameters in Neutrosophic Graphs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science R. Sundareswaran verfasserin aut G. Balaraman verfasserin aut P K Kishore Kumar verfasserin aut Said Broumi verfasserin aut In Neutrosophic Sets and Systems University of New Mexico, 2016 48(2022), Seite 109-121 (DE-627)1760646911 2331608X nnns volume:48 year:2022 pages:109-121 https://doi.org/10.5281/zenodo.6041365 kostenfrei https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c kostenfrei http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf kostenfrei https://doaj.org/toc/2331-6055 Journal toc kostenfrei https://doaj.org/toc/2331-608X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 48 2022 109-121
allfieldsSound	10.5281/zenodo.6041365 doi (DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c DE-627 ger DE-627 rakwb eng QA1-939 QA75.5-76.95 R.V. Jaikumar verfasserin aut Vulnerability Parameters in Neutrosophic Graphs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science R. Sundareswaran verfasserin aut G. Balaraman verfasserin aut P K Kishore Kumar verfasserin aut Said Broumi verfasserin aut In Neutrosophic Sets and Systems University of New Mexico, 2016 48(2022), Seite 109-121 (DE-627)1760646911 2331608X nnns volume:48 year:2022 pages:109-121 https://doi.org/10.5281/zenodo.6041365 kostenfrei https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c kostenfrei http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf kostenfrei https://doaj.org/toc/2331-6055 Journal toc kostenfrei https://doaj.org/toc/2331-608X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 48 2022 109-121
language	English
source	In Neutrosophic Sets and Systems 48(2022), Seite 109-121 volume:48 year:2022 pages:109-121
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topic_facet	score equitable sets strong score equitable sets equitable integrity strong equitable integrity Mathematics Electronic computers. Computer science
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authorswithroles_txt_mv	R.V. Jaikumar @@aut@@ R. Sundareswaran @@aut@@ G. Balaraman @@aut@@ P K Kishore Kumar @@aut@@ Said Broumi @@aut@@
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topic_title	QA1-939 QA75.5-76.95 Vulnerability Parameters in Neutrosophic Graphs score equitable sets strong score equitable sets equitable integrity strong equitable integrity
topic	misc QA1-939 misc QA75.5-76.95 misc score equitable sets misc strong score equitable sets misc equitable integrity misc strong equitable integrity misc Mathematics misc Electronic computers. Computer science
topic_unstemmed	misc QA1-939 misc QA75.5-76.95 misc score equitable sets misc strong score equitable sets misc equitable integrity misc strong equitable integrity misc Mathematics misc Electronic computers. Computer science
topic_browse	misc QA1-939 misc QA75.5-76.95 misc score equitable sets misc strong score equitable sets misc equitable integrity misc strong equitable integrity misc Mathematics misc Electronic computers. Computer science
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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hierarchy_parent_title	Neutrosophic Sets and Systems
hierarchy_parent_id	1760646911
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title	Vulnerability Parameters in Neutrosophic Graphs
ctrlnum	(DE-627)DOAJ08691989X (DE-599)DOAJae752adc74c34bc58a810f5e882d0a1c
title_full	Vulnerability Parameters in Neutrosophic Graphs
author_sort	R.V. Jaikumar
journal	Neutrosophic Sets and Systems
journalStr	Neutrosophic Sets and Systems
callnumber-first-code	Q
lang_code	eng
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publishDateSort	2022
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container_start_page	109
author_browse	R.V. Jaikumar R. Sundareswaran G. Balaraman P K Kishore Kumar Said Broumi
container_volume	48
class	QA1-939 QA75.5-76.95
format_se	Elektronische Aufsätze
author-letter	R.V. Jaikumar
doi_str_mv	10.5281/zenodo.6041365
author2-role	verfasserin
title_sort	vulnerability parameters in neutrosophic graphs
callnumber	QA1-939
title_auth	Vulnerability Parameters in Neutrosophic Graphs
abstract	Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds.
abstractGer	Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds.
abstract_unstemmed	Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, \|𝑠(𝑢)– 𝑠(𝑣)\| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{\|𝑆\| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds.
collection_details	GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700
title_short	Vulnerability Parameters in Neutrosophic Graphs
url	https://doi.org/10.5281/zenodo.6041365 https://doaj.org/article/ae752adc74c34bc58a810f5e882d0a1c http://fs.unm.edu/NSS/VulnerabilityParametersNeutrosophic9.pdf https://doaj.org/toc/2331-6055 https://doaj.org/toc/2331-608X
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author2	R. Sundareswaran G. Balaraman P K Kishore Kumar Said Broumi
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up_date	2024-07-03T23:26:12.237Z
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