Remarks on Multiplicative Atom-Bond Connectivity Index

The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC ind...
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Autor*in:	Riste Skrekovski [verfasserIn] Darko Dimitrov [verfasserIn] Jiemei Zhong [verfasserIn] Hualong Wu [verfasserIn] Wei Gao [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index

Übergeordnetes Werk:	In: IEEE Access - IEEE, 2014, 7(2019), Seite 76806-76811
Übergeordnetes Werk:	volume:7 ; year:2019 ; pages:76806-76811

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1109/ACCESS.2019.2920882

Katalog-ID:	DOAJ072093862

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520			\|a The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work.
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allfields	10.1109/ACCESS.2019.2920882 doi (DE-627)DOAJ072093862 (DE-599)DOAJ1fa2e86168334a7cbefa45f7727a8099 DE-627 ger DE-627 rakwb eng TK1-9971 Riste Skrekovski verfasserin aut Remarks on Multiplicative Atom-Bond Connectivity Index 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work. Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index Electrical engineering. Electronics. Nuclear engineering Darko Dimitrov verfasserin aut Jiemei Zhong verfasserin aut Hualong Wu verfasserin aut Wei Gao verfasserin aut In IEEE Access IEEE, 2014 7(2019), Seite 76806-76811 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:7 year:2019 pages:76806-76811 https://doi.org/10.1109/ACCESS.2019.2920882 kostenfrei https://doaj.org/article/1fa2e86168334a7cbefa45f7727a8099 kostenfrei https://ieeexplore.ieee.org/document/8731846/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2019 76806-76811
spelling	10.1109/ACCESS.2019.2920882 doi (DE-627)DOAJ072093862 (DE-599)DOAJ1fa2e86168334a7cbefa45f7727a8099 DE-627 ger DE-627 rakwb eng TK1-9971 Riste Skrekovski verfasserin aut Remarks on Multiplicative Atom-Bond Connectivity Index 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work. Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index Electrical engineering. Electronics. Nuclear engineering Darko Dimitrov verfasserin aut Jiemei Zhong verfasserin aut Hualong Wu verfasserin aut Wei Gao verfasserin aut In IEEE Access IEEE, 2014 7(2019), Seite 76806-76811 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:7 year:2019 pages:76806-76811 https://doi.org/10.1109/ACCESS.2019.2920882 kostenfrei https://doaj.org/article/1fa2e86168334a7cbefa45f7727a8099 kostenfrei https://ieeexplore.ieee.org/document/8731846/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2019 76806-76811
allfields_unstemmed	10.1109/ACCESS.2019.2920882 doi (DE-627)DOAJ072093862 (DE-599)DOAJ1fa2e86168334a7cbefa45f7727a8099 DE-627 ger DE-627 rakwb eng TK1-9971 Riste Skrekovski verfasserin aut Remarks on Multiplicative Atom-Bond Connectivity Index 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work. Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index Electrical engineering. Electronics. Nuclear engineering Darko Dimitrov verfasserin aut Jiemei Zhong verfasserin aut Hualong Wu verfasserin aut Wei Gao verfasserin aut In IEEE Access IEEE, 2014 7(2019), Seite 76806-76811 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:7 year:2019 pages:76806-76811 https://doi.org/10.1109/ACCESS.2019.2920882 kostenfrei https://doaj.org/article/1fa2e86168334a7cbefa45f7727a8099 kostenfrei https://ieeexplore.ieee.org/document/8731846/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2019 76806-76811
allfieldsGer	10.1109/ACCESS.2019.2920882 doi (DE-627)DOAJ072093862 (DE-599)DOAJ1fa2e86168334a7cbefa45f7727a8099 DE-627 ger DE-627 rakwb eng TK1-9971 Riste Skrekovski verfasserin aut Remarks on Multiplicative Atom-Bond Connectivity Index 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work. Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index Electrical engineering. Electronics. Nuclear engineering Darko Dimitrov verfasserin aut Jiemei Zhong verfasserin aut Hualong Wu verfasserin aut Wei Gao verfasserin aut In IEEE Access IEEE, 2014 7(2019), Seite 76806-76811 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:7 year:2019 pages:76806-76811 https://doi.org/10.1109/ACCESS.2019.2920882 kostenfrei https://doaj.org/article/1fa2e86168334a7cbefa45f7727a8099 kostenfrei https://ieeexplore.ieee.org/document/8731846/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2019 76806-76811
allfieldsSound	10.1109/ACCESS.2019.2920882 doi (DE-627)DOAJ072093862 (DE-599)DOAJ1fa2e86168334a7cbefa45f7727a8099 DE-627 ger DE-627 rakwb eng TK1-9971 Riste Skrekovski verfasserin aut Remarks on Multiplicative Atom-Bond Connectivity Index 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work. Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index Electrical engineering. Electronics. Nuclear engineering Darko Dimitrov verfasserin aut Jiemei Zhong verfasserin aut Hualong Wu verfasserin aut Wei Gao verfasserin aut In IEEE Access IEEE, 2014 7(2019), Seite 76806-76811 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:7 year:2019 pages:76806-76811 https://doi.org/10.1109/ACCESS.2019.2920882 kostenfrei https://doaj.org/article/1fa2e86168334a7cbefa45f7727a8099 kostenfrei https://ieeexplore.ieee.org/document/8731846/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2019 76806-76811
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callnumber-first	T - Technology
author	Riste Skrekovski
spellingShingle	Riste Skrekovski misc TK1-9971 misc Chemical graph theory misc atom-bond connectivity misc multiplicative atom-bond connectivity index misc Electrical engineering. Electronics. Nuclear engineering Remarks on Multiplicative Atom-Bond Connectivity Index
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topic_title	TK1-9971 Remarks on Multiplicative Atom-Bond Connectivity Index Chemical graph theory atom-bond connectivity multiplicative atom-bond connectivity index
topic	misc TK1-9971 misc Chemical graph theory misc atom-bond connectivity misc multiplicative atom-bond connectivity index misc Electrical engineering. Electronics. Nuclear engineering
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title	Remarks on Multiplicative Atom-Bond Connectivity Index
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title_auth	Remarks on Multiplicative Atom-Bond Connectivity Index
abstract	The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work.
abstractGer	The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work.
abstract_unstemmed	The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants that are found in a vast variety of chemical applications. This paper is devoted to establishing some extremal results regarding the variant of the ABC index, the so-called multiplicative ABC index (ABC$\Pi $ ), which, for a graph $G$ , is defined as ${{ ABC}}\Pi (G)=\prod _{uv\in E(G)}\sqrt {\frac {d(u)+d(v)-2}{d(u)d(v)}}$ . We have shown that the complete graph $K_{n}$ has a minimum ABC$\Pi $ index among connected simple graphs with $n$ vertices, while the star graph $S_{n-1}$ has the maximum ABC$\Pi $ index. As $S_{n-1}$ attains the maximum amongst bipartite graphs on $n$ vertices, we additionally show that the bipartite complete balanced graph $K_{\left \lfloor{ n/2 }\right \rfloor, \left \lceil{ n/2 }\right \rceil }$ attains the minimum in this class of graphs. As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work.
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title_short	Remarks on Multiplicative Atom-Bond Connectivity Index
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score	7.402693

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Remarks on Multiplicative Atom-Bond Connectivity Index

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