On the maximum (signless) Laplacian spectral radius of the cacti
Suppose that the vertex set of a graph G is VG) = 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 QAG) = DG) + A(G) and LaG) = D(G) - AG) 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. , journal=Utilitas Mathematica , author=Fan, Dandan and Mu, Shanzhi and Chen, Hua and Wang, Guoping, year=2018, month=Nov.