Published in

Elsevier, Linear Algebra and its Applications, 8-10(433), p. 1561-1572, 2010

DOI: 10.1016/j.laa.2010.06.007

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On the spectral radius of quasi-k-cyclic graphs

Journal article published in 2010 by Xianya Geng, Shuchao Li, Slobodan K. Simić
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

A connected graph G = (V(G), E(G)) is called a quasi-k-cyclic graph, if there exists a vertex q is an element of V(G) such that G - q is a k-cyclic graph (connected with cyclomatic number k). In this paper we identify in the set of quasi-k-cyclic graphs (for k <= 3) those graphs whose spectral radius of the adjacency matrix (and the signless Laplacian if k <= 2) is the largest. In addition, for quasi-unicyclic graphs we identify as well those graphs whose spectral radius of the adjacency matrix is the second largest.