The D-distance between vertices of a graph G is obtained by considering the path lengths and as well as the degrees of vertices present on the path. The average D-distance of a connected graph is the average of the D-distance between all pairs of vertices of the graph. Similarly, the average edge D-distance is the average of D-distances between all pairs of edges in the graph. In this article we study the average edge D-distance of a graph. We find bounds for average edge D-distance which are sharp and also prove some other results.
Keywords
Average D-Distance, D-Distance, Diameter, 2000 Mathematics Subject Classifications, 05C12.
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