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

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, this name comes from the fact that $Q(H)$ is exactly the well-known signless Laplacian matrix for $2$-graph. Define the largest eigenvalue $\rho(H)$ of $Q(H)$ as the spectral radius of $H$. In this paper, we give some lower and upper bounds on $\rho(H)$ by some structural parameters (such as independent number, maximum degree, minimum degree, diameter, and so on) of $H$, which are extend or improve some known results.