Rad HAZU, Matematičke znanosti, Vol. 24 (2020), 1-14.

LAPLACIAN COEFFICIENTS OF TREES

Ali Ghalavand and Ali Reza Ashrafi

Abstract.   Let G be a simple and undirected graph with Laplacian polynomial ψ(G, λ) = Σ_k=0ⁿ (-1)^n-kc_k(G)λ^k. In this paper, exact formulas for the coefficient c_n-4 and the number of 4-matchings with respect to the Zagreb indices of a given tree are presented. The chemical trees with first through the fifteenth greatest c_n-4-values are also determined.

2020 Mathematics Subject Classification.   05C31, 05C05.

Key words and phrases.   Laplacian coefficient, matching, Zagreb index, tree.

DOI: https://doi.org/10.21857/m16wjcev89

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