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

zbMATH Open1340.05183arXiv1306.1386MaRDI QIDQ3462399

Jieshan Yang, Lihua You

Publication date: 14 January 2016

Abstract: For a graph $G$ and a non-zero real number $alpha$, the graph invariant $S_{alpha}(G)$ is the sum of the $alph{a}^{th}$ 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.

Full work available at URL: https://arxiv.org/abs/1306.1386

zbMATH Keywords

bipartite graphconnectivitysignless Laplacian matrix

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Connectivity (05C40)

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