Further results on the star degree of graphs

Tingzeng Wu, Tian Zhou and Huazhong Lü

Applied Mathematics and Computation, 2022, vol. 425, issue C

Abstract: Let G be any simple undirected graph and let Q(G) be the signless Laplacian matrix of G. The polynomial ϕ(Q(G),x)=per(xI−Q(G)) is called the signless Laplacian permanental polynomial of G. The star degree of a graph G is the multiplicity of root 1 of ϕ(Q(G),x). Faria (1985) first considered the star degree of graphs. Based on Faria’s results, we further study the features of star degree of graphs, and give a formula to compute the star degree of a graph by a vertex partition of the graph. As applications, we derive the star degree set of n-vertex graphs, and we determine the graphs with extremal star degree. Furthermore, we show that some graphs with given star degree are determined by their signless Laplacian permanental spectra.

Keywords: Permanent; Permanental root; Star degree; Signless Laplacian permanental spectrum; Signless Laplacian cospectral (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001606

DOI: 10.1016/j.amc.2022.127076

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