On the maximum (signless) Laplacian spectral radius of the cacti
Abstract
Suppose that the vertex set of a graph G is V{G) = {vi9v2, •.., Vn}. Then we denote by dy.(G) the degree of t\ in G. Let A(G) be the adjacent matrix of G and D(G) be the n x n diagonal matrix with its (iyt)-entry equal to dVi(G). Then QA{G) = D{G) + A(G) and La{G) = D(G) - A{G) are the signless Laplacian matrix and Laplacian matrix of G} respectively. The signless Laplacian and Laplacian spectral radius of G are respectively the largest eigenvalue of Qa(G) and L/[(G). In this paper we characterize the graphs with the maximum signless Laplacian spectral radius and the maximum Laplacian spectral radius respectively a- mong all cacti of order n with given k cycles or r pendent vertices. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.
