More on Sombor Index of Graphs

Wenjie Ning, Yuheng Song and Kun Wang
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Wenjie Ning: College of Science, China University of Petroleum (East China), Qingdao 266580, China
Yuheng Song: College of Science, China University of Petroleum (East China), Qingdao 266580, China
Kun Wang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2022, vol. 10, issue 3, 1-12

Abstract: Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G = ( V ( G ) , E ( G ) ) be a graph. Then, the Sombor index of G is defined as S O ( G ) = ∑ u v ∈ E ( G ) d G 2 ( u ) + d G 2 ( v ) . In this paper, we give some lemmas that can be used to compare the Sombor indices between two graphs. With these lemmas, we determine the graph with maximum S O among all cacti with n vertices and k cut edges. Furthermore, the unique graph with maximum S O among all cacti with n vertices and p pendant vertices is characterized. In addition, we find the extremal graphs with respect to S O among all quasi-unicyclic graphs.

Keywords: topological index; vertex degree; Sombor index; cactus; quasi-unicyclic graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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