Connectivity, diameter, minimal degree, independence number and the eccentric distance sum of graphs

Chen, Shuya; Li, Shuchao; Wu, Yueyu; Sun, Lingli

doi:10.1016/j.dam.2018.03.057

Cited by 8 publications

(1 citation statement)

References 13 publications

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“…ξ c was introduced by Sharma, Goswami, and Madan [17], ξ d by Gupta, Singh, and Madan [7], and DD by Dobrynin and Kochetova [6] and by Gutman [8]. These three topological indices are well investigated, selected contrubutions to the eccentric connectivity index are [10,13,22], to the eccentric distance sum [1,14,21], and to the degree distance [15,18,19]. The three invariants were also compared to other invariants, cf.…”

Section: Introductionmentioning

confidence: 99%

On the difference between the eccentric connectivity index and eccentric distance sum of graphs

Alizadeh¹,

Klavžar²

2020

Preprint

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The eccentric connectivity index of a graph and D(v) the sum of distances between v and the other vertices. A lower and an upper bound on ξ d (G) − ξ c (G) is given for an arbitrary graph G. Regular graphs with diameter at most 2 and joins of cocktail-party graphs with complete graphs form the graphs that attain the two equalities, respectively. Sharp lower and upper bounds on ξ d (T ) − ξ c (T ) are given for arbitrary trees. Sharp lower and upper bounds on ξ d (G) + ξ c (G) for arbitrary graphs G are also given, and a sharp lower bound on ξ d (G) for graphs G with a given radius is proved.

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Section: Introductionmentioning

confidence: 99%

On the difference between the eccentric connectivity index and eccentric distance sum of graphs

Alizadeh¹,

Klavžar²

2020

Preprint

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The connective eccentricity index of graphs and its applications to octane isomers and benzenoid hydrocarbons

Wang

Yan

Zaman

et al. 2020

Int J of Quantum Chemistry

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The connective eccentricity index (CEI) of a graph G is defined as , where εG(.) denotes the eccentricity of the corresponding vertex. The CEI obligates an influential ability, which is due to its estimating pharmaceutical properties. In this paper, we first characterize the extremal graphs with respect to the CEI among k‐connected graphs (k‐connected bipartite graphs) with a given diameter. Then, the sharp upper bound on the CEI of graphs with given connectivity and minimum degree (independence number) is determined. Finally, we calculate the CEI of two sets of molecular graphs: octane isomers and benzenoid hydrocarbons. We compare their CEI with some other distance‐based topological indices through their correlations with the chemical properties. The linear model for the CEI is better than or as good as the models corresponding to the other distance‐based indices.

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On the Difference Between the Eccentric Connectivity Index and Eccentric Distance Sum of Graphs

Alizadeh

Klavžar

2020

Bull. Malays. Math. Sci. Soc.

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Connectivity, diameter, minimal degree, independence number and the eccentric distance sum of graphs

Cited by 8 publications

References 13 publications

On the difference between the eccentric connectivity index and eccentric distance sum of graphs

On the difference between the eccentric connectivity index and eccentric distance sum of graphs

The connective eccentricity index of graphs and its applications to octane isomers and benzenoid hydrocarbons

On the Difference Between the Eccentric Connectivity Index and Eccentric Distance Sum of Graphs

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