On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Fixed Diameter

Abstract

Let $G$ be a bicyclic graph. Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. In this paper, we determine the graph with the maximal signless Laplacian spectral radius among all the bicyclic graphs with $n$ vertices and diameter $d$.