On the Spectral Radius of Graphs with \(k\)-Vertex Cut

Guoping Wang1,2, Qiongxiang Huang3, Jing Cai1
1Department of Mathematics, Xinjiang Normal University, Urumai, Xinjiang 830000, P.R.China
2Department of Mathematics, Jiangsu Teachers University of Technology, Changzhou, Jiangsu 213001, P.R.China
3The College of Mathematics and Systems Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P.R.China

Abstract

We study the spectral radius of graphs with \(n\) vertices and a \(k\)-vertex cut and describe the graph which has the maximal spectral radius in this class. We also discuss the limit point of the maximal spectral radius.