Extremal Sombor Index of Graphs with Cut Edges and Clique Number
Author:
Wali Mihrigul12,
Guji Raxida2
Affiliation:
1. School of Mathematical Science, Xiamen University, Xiamen 361005, China
2. School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China
Abstract
The Sombor index is defined as SO(G)=∑uv∈E(G)d2(u)+d2(v), where d(u) and d(v) represent the number of edges in the graph G connected to the vertices u and v, respectively. In this paper, we characterize the largest and second largest Sombor indexes with a given number of cut edges. Moreover, we determine the upper and lower sharp bounds of the Sombor index with a given number of clique numbers, and we characterize the extremal graphs.
Funder
Research Fund of Xinjiang University of Finance and Economics
Base Tender Project of Humanities, Social Sciences, funded by the Ministry of Education
Natural Science Foundation of Xinjiang Uyghur Autonomous Region
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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