Some bounds on spectral radius of signless Laplacian matrix of k-graphs

¹ School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, P.R. China
² College of Preparatory Education, South-Central Minzu University, Wuhan 430074, P.R. China

^* Corresponding author: 987682282@qq.com; zzxun73@163.com

Received: 15 March 2023
Accepted: 17 July 2023

Abstract

For a k-graph H = (V(H), E(H)), let B(H) be its incidence matrix, and Q(H) = B(H)B(H)^T be its signless Laplacian matrix, and this name comes from the fact that Q(H) is exactly the well-known signless Laplacian matrix for 2-graph. Define the largest eigenvalue ρ(H) of Q(H) as the spectral radius of H. In this paper, we give some lower and upper bounds on ρ(H) using some structural parameters (such as independent number, maximum degree, minimum degree, diameter, and so on) of H, which extended or improved some known results.