Affiliation:
1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Abstract
In this paper, we present the upper and lower bounds on Sombor index SO(G) among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on SO(G) among connected graphs in terms of some parameters, including chromatic, girth and matching number. Meanwhile, we characterize the extremal graphs attaining those bounds. In addition, we give upper bounds on SO(G) among connected bipartite graphs with given matching number and/or connectivity and determine the corresponding extremal connected bipartite graphs.
Funder
Natural Science Foundation of Xinjiang
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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