科研之友
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摘要
Let G be a connected graph with vertex set V (G). The degree distance of G is defined as D'(G) = Sigma({u,v}subset of V(G)) (deg(G)(u) + deg(G)(v))d(u, v), where deg(G)(u) is the degree of vertex u, and d(u, u) denotes the distance between u and v. Here we characterize n-vertex unicyclic graphs with girth k, having minimum and maximum degree distance, respectively. Furthermore, we prove that the graph B-n obtained from two triangles linked by a path, is the unique graph having the maximum degree distance among bicyclic graphs, which resolves a recent conjecture of Tomescu.
