Research article

On the graph connectivity and the variable sum exdeg index

  • Received: 27 July 2020 Accepted: 20 October 2020 Published: 23 October 2020
  • MSC : 05C07, 05C35, 92E10

  • Topological indices are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. The variable sum exdeg index $SEI_{a}(G)$ of a graph $G$ is defined as $\sum _{u\in V(G)}d_{G}(u)a^{d_{G}(u)}$, where $d_{G}(u)$ is the degree of vertex $u$ and $a$ is an arbitrary positive real number different from 1. In this paper, we obtain the extremal values of the variable sum exdeg indices (for $a>1$) in terms of the number of cut edges, or the number of cut vertices, or the vertex connectivity, or the edge connectivity of a graph. Furthermore, the corresponding extremal graphs are characterized.

    Citation: Jianwei Du, Xiaoling Sun. On the graph connectivity and the variable sum exdeg index[J]. AIMS Mathematics, 2021, 6(1): 607-622. doi: 10.3934/math.2021037

    Related Papers:

  • Topological indices are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. The variable sum exdeg index $SEI_{a}(G)$ of a graph $G$ is defined as $\sum _{u\in V(G)}d_{G}(u)a^{d_{G}(u)}$, where $d_{G}(u)$ is the degree of vertex $u$ and $a$ is an arbitrary positive real number different from 1. In this paper, we obtain the extremal values of the variable sum exdeg indices (for $a>1$) in terms of the number of cut edges, or the number of cut vertices, or the vertex connectivity, or the edge connectivity of a graph. Furthermore, the corresponding extremal graphs are characterized.


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