On the Sombor index of graphs with given connectivity and number of bridges

2022/08/22 by Hayat, Sakander, Arshad, Muhammad, Das, Kinkar Chandra
#05C09 #05C35 #05C92 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.09993

Abstract

Recently in 2021, Gutman introduced the Sombor index of a graph, a novel degree-based topological index. It has been shown that the Sombor index efficiently models the thermodynamic properties of chemical compounds. Assume \mathbbB_n^k (resp. \mathbbV_n^k) comprises all graphs with order n having number of bridges (resp. vertex-connectivity) k. Horoldagva & Xu (2021) characterized graphs achieving the maximum Sombor index of graphs in \mathbbB_n^k. This paper characterizes graphs achieving the minimum Sombor index in \mathbbB_n^k. Certain auxiliary operation on graphs in \mathbbB_n^k are introduced and employed for the characterization. Moreover, we characterize graphs achieving maximum Sombor index in \mathbbV_n^k. ome open problems, which naturally arise from this work, have been proposed at the end.

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