Let Diag(G) and D(G) be the degree-diagonal matrix and distance matrix of G, respectively. Define the multiplier Diag(G)D(G) as degree distance matrix of G. The degree distance of G is defined as D'(G) = Σ x∈v(G)dG(x)Dg(x), where dg(x) is the degree of vertex x, DG(x) = Σ∈V(G)d G(u,x) and dg(u,x) the distance between u and x. Obviously, D'(G) is also the sum of elements of degree distance matrix Diag(G)D(G) of G. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G (n, r) be the set of cacti of orde...
