文献类型：期刊文献

英文题名：A unified approach to the spectral radius, connectivity and edge-connectivity of graphs

作者：Wang, Yu[1]; Li, Dan[1]; Lin, Huiqiu[1,2]

机构：[1] College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2024

外文期刊名：arXiv

收录：EI(收录号：20240247413)

语种：英文

外文关键词：Matrix algebra

摘要：For two integers r ≥ 2 and h ≥ 0, the h-extra r-component connectivity κhr (G) of a graph G is defined to be the minimum size of a subset of vertices whose removal disconnects G, and there are at least r connected components in G?S and each component has at least h + 1 vertices. Denote by Gκhrn,δ the set of graphs with h-extra r-component connectivity κhr (G) and minimum degree δ. The following problem concerning spectral radius was proposed by Brualdi and Solheid [On the spectral radius of complementary acyclic matrices of zeros and one, SIAM J. Algebra Discrete Methods 7 (1986) 265-272]: Given a set of graphs L, find an upper bound for the spectral radius of graphs in L and characterize the graphs in which the maximal spectral radius is attained. We study this question for L = Gκhrn,δ where r ≥ 2 and h ≥ 0. Fan, Gu and Lin [l-connectivity, l-edge-connectivity and spectral radius of graphs, arXiv:2309.05247] give the answer to r ≥ 2 and h = 0. In this paper, we solve this problem completely for r ≥ 2 and h ≥ 1. Moreover, we also investigate analogous problems for the edge version. Our results can break the restriction of the extremum structure of the conditional connectivity. This implies some previous results in connectivity and edge-connectivity. Copyright ? 2024, The Authors. All rights reserved.