Notes on the sum of powers of the signless Laplacian eigenvalues of graphs

Abstract

For a graph $G$ and a non-zero real number $\alpha$, the graph invariant $S_{\alpha }(G)$ is the sum of the ${\alpha }^{th}$ power of the non-zero signless Laplacian eigenvalues of $G$. In this paper, we obtain the sharp bounds of $S_{\alpha }(G)$ for a connected bipartite graph $G$ on $n$ vertices and a connected graph $G$ on $n$ vertices having a connectivity less than or equal to $k$, respectively, and propose some open problems for future research.

arXiv comment9 pages

References in corpus (1)

• On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs

Cited by in corpus (1)

• On two conjectures on sum of the powers of signless Laplacian eigenvalues of a graph