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.