摘要 : Given a graph G = (V, E) with vertex set V and edge set E, we extend the concept of k-matching number and Hosoya index to a weighted graph (G; omega), where omega is a weight function defined over E. In particular, if phi is a ver... 展开 Given a graph G = (V, E) with vertex set V and edge set E, we extend the concept of k-matching number and Hosoya index to a weighted graph (G; omega), where omega is a weight function defined over E. In particular, if phi is a vertex-degree-based (VDB) topological index defined via phi = phi(G) = Sigma(uv is an element of E) phi d(G)(u),d(G)(v), where d(G)(u) is the degree of the vertex u and phi(i,j) is an appropriate function with the property phi(i,j) = phi(j,i), then we consider the weighted graph (G; phi) with weight function phi : E -> R defined as phi(uv) = phi d(G)(u),d(G)(v), for all uv is an element of E. It turns out that m((G; phi), 1), the number of weighted 1-matchings in (G; phi), is precisely phi(G), and for k >= 2, the k-matching numbers m((G; phi), k) can be viewed as new kth order VDB-Hosoya indices. Later, we consider the extremal value problem of the Hosoya index over the set {T-n; phi} = {(T; phi) : T is an element of T-n}, where T-n is the set of trees with n vertices. (C) 2022 Elsevier B.V. All rights reserved. 收起