Signless Laplacian spectral radius of graphs without short cycles or long cycles

DOI10.1016/J.LAA.2022.03.011arXiv2305.03280MaRDI QIDQ6435437

Bing Wang, Ming-qing Zhai, Wenwen Chen

Publication date: 5 May 2023

Abstract: The signless Laplacian spectral radius of a graph $G$, denoted by $q(G)$, is the largest eigenvalue of its signless Laplacian matrix. In this paper, we investigate extremal signless Laplacian spectral radius for graphs without short cycles or long cycles. Let $mathcalG(m,g)$ be the family of graphs on $m$ edges with girth $g$ and $mathcalH(m,c)$ be the family of graphs on $m$ edges with circumference $c$. More precisely, we obtain the unique extremal graph with maximal $q(G)$ in $mathcalG(m,g)$ and $mathcalH(m,c)$, respectively.

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

This page was built for publication: Signless Laplacian spectral radius of graphs without short cycles or long cycles

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6435437)