Maximum Degree Distance of Graphs with Exactly Two Cycles

The degree distance of a connected graph G with vertex set V (G) is defined as D 0 (G) = P u2 V (G) d G(u)DG(u), where dG(u) is the degree of vertex u and DG(u) is the sum of distances between u and all vertices of G. We determine the maximum degree distances in the class of connected graphs with exactly two vertex–disjoint cycles and in the class of connected graphs with exactly two cycles of a common vertex, respectively, and then the maximum degree distance in the class of connected graphs with exactly two cycles. The extremal graphs are characterized.