Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices

Abeer M. Albalahi, Akbar Ali, Tayyba Zafar, Wael W. Mohammed and Junwei Wang

Discrete Dynamics in Nature and Society, 2021, vol. 2021, 1-4

Abstract: A bond incident degree (BID) index of a graph G is defined as ∑uv∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG is the edge set of G, and f is a real-valued symmetric function. The choice fdGu,dGv=adGu+adGv in the aforementioned formula gives the variable sum exdeg index SEIa, where a≠1 is any positive real number. A cut vertex of a graph G is a vertex whose removal results in a graph with more components than G has. A graph of maximum degree at most 4 is known as a molecular graph. Denote by Vn,k the class of all n-vertex graphs with k≥1 cut vertices and containing at least one cycle. Recently, Du and Sun [AIMS Mathematics, vol. 6, pp. 607–622, 2021] characterized the graphs having the maximum value of SEIa from the set Vnk for a>1. In the present paper, we not only characterize the graphs with the minimum value of SEIa from the set Vnk for a>1, but we also solve a more general problem concerning a special type of BID indices. As the obtained extremal graphs are molecular graphs, they remain extremal if one considers the class of all n-vertex molecular graphs with k≥1 cut vertices and containing at least one cycle.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:9970254

DOI: 10.1155/2021/9970254

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