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The connective eccentricity index of graphs and its applications to octane isomers and benzenoid hydrocarbons
Author(s) -
Wang Guangfu,
Yan Lixia,
Zaman Shahid,
Zhang Minjie
Publication year - 2020
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26334
Subject(s) - octane , topological index , bipartite graph , combinatorics , vertex (graph theory) , eccentricity (behavior) , wiener index , graph , mathematics , chemistry , organic chemistry , political science , law
The connective eccentricity index (CEI) of a graph G is defined as ξ ee G = ∑ xy ∈ E G1 ε G x+ 1 ε G y, where ε G (.) 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.