where r is the molecular graph13 considered, possessing N = N ( r ) vertices. Further, A is the ( N X N dimensional) adjacency matrix,13 D is the ( N X N dimensional) distance matrix,13J4 and v =… (More)

Let G be a graph with n vertices and m edges. Let λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, . . . , μn be the eigenvalues of the Laplacian matrix of G. An… (More)

Let G be a graph with vertex set V (G) and edge set E(G) . The first and second multiplicative Zagreb indices of G are Π1 = ∏ x∈V (G) deg(x) 2 and Π2 = ∏ xy∈E(G) deg(x) deg(y) , respectively, where… (More)

The Wiener index ( W) and the Hosoya polynomial ( H) have been calculated for all trees (and thus for all chemical trees) with 20 and fewer vertices. Corroborating an earlier observation (Razinger,… (More)

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. We define the matching energy (ME) of the graph G as the sum of the absolute values of the zeros of the… (More)

The atom–bond connectivity index (ABC) is a vertex–degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i ,… (More)

If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index We of G is then equal… (More)