Some tight bounds for the harmonic index and the variation of the Randić index of graphs
The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the h...
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| Autor*in: |
Deng, Hanyuan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019transfer abstract |
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| Schlagwörter: |
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| Umfang: |
6 |
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| Übergeordnetes Werk: |
Enthalten in: A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations - Guo, Bangwei ELSEVIER, 2023, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:342 ; year:2019 ; number:7 ; pages:2060-2065 ; extent:6 |
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| DOI / URN: |
10.1016/j.disc.2019.03.022 |
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| 520 | |a The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. | ||
| 520 | |a The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. | ||
| 650 | 7 | |a Harmonic index |2 Elsevier | |
| 650 | 7 | |a Randić index |2 Elsevier | |
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| 700 | 1 | |a Balachandran, Selvaraj |4 oth | |
| 700 | 1 | |a Elumalai, Suresh |4 oth | |
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10.1016/j.disc.2019.03.022 doi GBV00000000000624.pica (DE-627)ELV04678022X (ELSEVIER)S0012-365X(19)30109-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Deng, Hanyuan verfasserin aut Some tight bounds for the harmonic index and the variation of the Randić index of graphs 2019transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. Harmonic index Elsevier Randić index Elsevier Degree Elsevier Balachandran, Selvaraj oth Elumalai, Suresh oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:7 pages:2060-2065 extent:6 https://doi.org/10.1016/j.disc.2019.03.022 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 7 2060-2065 6 |
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10.1016/j.disc.2019.03.022 doi GBV00000000000624.pica (DE-627)ELV04678022X (ELSEVIER)S0012-365X(19)30109-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Deng, Hanyuan verfasserin aut Some tight bounds for the harmonic index and the variation of the Randić index of graphs 2019transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. Harmonic index Elsevier Randić index Elsevier Degree Elsevier Balachandran, Selvaraj oth Elumalai, Suresh oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:7 pages:2060-2065 extent:6 https://doi.org/10.1016/j.disc.2019.03.022 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 7 2060-2065 6 |
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10.1016/j.disc.2019.03.022 doi GBV00000000000624.pica (DE-627)ELV04678022X (ELSEVIER)S0012-365X(19)30109-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Deng, Hanyuan verfasserin aut Some tight bounds for the harmonic index and the variation of the Randić index of graphs 2019transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. Harmonic index Elsevier Randić index Elsevier Degree Elsevier Balachandran, Selvaraj oth Elumalai, Suresh oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:7 pages:2060-2065 extent:6 https://doi.org/10.1016/j.disc.2019.03.022 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 7 2060-2065 6 |
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10.1016/j.disc.2019.03.022 doi GBV00000000000624.pica (DE-627)ELV04678022X (ELSEVIER)S0012-365X(19)30109-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Deng, Hanyuan verfasserin aut Some tight bounds for the harmonic index and the variation of the Randić index of graphs 2019transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. Harmonic index Elsevier Randić index Elsevier Degree Elsevier Balachandran, Selvaraj oth Elumalai, Suresh oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:7 pages:2060-2065 extent:6 https://doi.org/10.1016/j.disc.2019.03.022 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 7 2060-2065 6 |
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10.1016/j.disc.2019.03.022 doi GBV00000000000624.pica (DE-627)ELV04678022X (ELSEVIER)S0012-365X(19)30109-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Deng, Hanyuan verfasserin aut Some tight bounds for the harmonic index and the variation of the Randić index of graphs 2019transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. Harmonic index Elsevier Randić index Elsevier Degree Elsevier Balachandran, Selvaraj oth Elumalai, Suresh oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:7 pages:2060-2065 extent:6 https://doi.org/10.1016/j.disc.2019.03.022 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 7 2060-2065 6 |
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Enthalten in A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations Amsterdam [u.a.] volume:342 year:2019 number:7 pages:2060-2065 extent:6 |
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Some tight bounds for the harmonic index and the variation of the Randić index of graphs |
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The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. |
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The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. |
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The harmonic index H G and the variation of the Randić index R ′ ( G ) of a graph G are defined as the sum of the weights 2 d u + d v and 1 m a x d u , d v over all the edges u v of G , respectively, where d u denotes the degree of a vertex u in G . In this paper, we give some tight bounds for the harmonic index (or the variation of the Randić index, respectively) of G in terms of its maximum and minimum degree mean rates over its edges, where the degree mean rate is γ H ( e ) = 2 d u d v ( d u + d v ) 2 (or γ R ′ ( e ) = m i n { d u , d v } d u + d v , respectively) of an edge e = u v ∈ E . We use the same method given by Dalfó (2018) recently, which proved the conjecture by Fajtlowicz that states that the average distance is bounded above by the Randić index, for graphs with order n large enough when δ is greater than (approximately) Δ 1 3 , where Δ is the maximum degree. |
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Some tight bounds for the harmonic index and the variation of the Randić index of graphs |
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