Coefficients of the characteristic polynomial of the (signless, normalized) Laplacian of a graph
Researchers worldwide were rigorously looking for isomorphism invariants and their endeavor has culminated in the development of algebraic properties of the different matrices of a graph such as adjacency matrix, signless matrix, Laplacian matrix, normalized matrix and so on. Specifically, they studied in deep the coefficients of the characteristic polynomial of these matrices. From their analysis, the authors give the fifth coefficient of the Laplacian characteristic polynomial and of the signless Laplacian characteristic polynomial and the first five coefficients of the normalized Laplacian characteristic polynomial of a graph. The authors draw inspiration from the result of Kelmans that Laplacian coefficients can be expressed in terms of subtree structures of \(G\) (see [\textit{A. K. Kelmans} and \textit{V. M. Chelnokov}, J. Comb. Theory, Ser. B 16, 197--214 (1974; Zbl 0277.05104)]). The results are quite interesting and easily comprehensible.
scientific article; zbMATH DE number 6817808