Kannan, Balakrishnan; Bresar, B; Manoj, Changat; Klavzar, S; Kovse, M; Subhamathi, A R(Wiley Subscription Services, Inc., A Wiley Company, September 1, 2010)
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Abstract:
The distance DG(v) of a vertex v in an undirected graph G is the sum of the
distances between v and all other vertices of G. The set of vertices in G with maximum
(minimum) distance is the antimedian (median) set of a graph G. It is proved that for
arbitrary graphs G and J and a positive integer r 2, there exists a connected graph H
such that G is the antimedian and J the median subgraphs of H, respectively, and that
dH(G, J) = r. When both G and J are connected, G and J can in addition be made
convex subgraphs of H.