On the Signless Laplacian Spectral Radius of Tricyclic Graphs with \(n\) Vertices and Diameter \(d\)

Xinying Pai1,2, Sanyang Liu1
1Department of Mathematics, Xidian University, Xi’an, Shanxi 710071, P. R. China
2College of science, China University of Petroleum, Qingdao, Shandong 266580, P. R. China

Abstract

Let \(G\) be a tricyclic graph. Tricyclic graphs are connected graphs in which the number of edges equals the number of vertices plus two. In this paper, we determine graphs with the largest signless Laplacian spectral radius among all the tricyclic graphs with \(n\) vertices and diameter \(d\).