On Wiener Index of Graph Complements
نویسندگان
چکیده
Let G be an (n, m)-graph. We say that G has property (∗) if for every pair of its adjacent vertices x and y, there exists a vertex z, such that z is not adjacent to either x or y. If the graph G has property (∗), then its complement G is connected, has diameter 2, and its Wiener index is equal to ( n 2 ) + m, i.e., the Wiener index is insensitive of any other structural details of the graph G. We characterize numerous classes of graphs possessing property (∗), among which are trees, regular, and unicyclic graphs.
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