Average D-Distance Between Edges of a Graph

D. Reddy Babu; P. L. N. Varma

doi:10.17485/ijst/2015/v8i2/67357

Average D-Distance Between Edges of a Graph

Affiliations
1 Department of Mathematics, Koneru Lakshmaiah Education Foundation (K.L. University), Vaddeswaram, Guntur 522 502, India
2 Department of Science & Humanities, Vignan's Foundation for Science, Technology and Research University, Vadlamudi, Guntur 522 213, India

Abstract
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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.