On the degree distance of a graph |
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Authors: | P. Dankelmann I. Gutman H.C. Swart |
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Affiliation: | a University of KwaZulu-Natal, Durban, South Africa b University of Kragujevac, Kragujevac, Serbia |
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Abstract: | If G is a connected graph with vertex set V, then the degree distance of G, D′(G), is defined as , where degw is the degree of vertex w, and d(u,v) denotes the distance between u and v. We prove the asymptotically sharp upper bound for graphs of order n and diameter d. As a corollary we obtain the bound for graphs of order n. This essentially proves a conjecture by Tomescu [I. Tomescu, Some extremal properties of the degree distance of a graph, Discrete Appl. Math. (98) (1999) 159-163]. |
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Keywords: | Distance Degree distance Diameter |
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