Convex (anti)median Subgraphs of Graphs
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چکیده
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. In this note we prove that for every connected graph G there exists a graph H such that G is a convex subgraph of H and V (G) is the antimedian set of H . A similar construction for G as a convex median subgraph is also presented.
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تاریخ انتشار 2008