The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices and k pendant vertices

Abstract

A connected graph is called a c-cyclic graph if it contains n vertices and n + c 1 edges. Let C(n,k,c) denote the class of connected c-cyclic graphs with n vertices and k pendant vertices. Recently, the unique extremal graph, which has greatest (respectively, signless) Laplacian spectral radius, in C(n,k,c) has been determined for 0 � c � 3, k � 1 and n � 2c + k + 1. In this paper, the unique graph with greatest (respectively, signless) Laplacian spectral radius in C(n,k,c) is determined for c � 0, k � 1 and n � 2c + k + 1.