The w ‐median of a connected strongly chordal graph

Suppose G = (V, E) is a graph in which every vertex x has a non‐negative real number w(x) as its weight. The w ‐distance sum of a vertex y is D G, w (y) = σ x≅v d(y, x)w(x). The w ‐median of G is the set of all vertices y with minimum w ‐distance sum D G,w (y). This paper shows that the w ‐median of a connected strongly chordal graph G is a clique when w(x) is positive for all vertices x in G .