Average D-distance Between Edges of a Graph

D  Reddy Babu   and P  L  N  Varma

doi:10.17485/ijst/2015/v8i2/58066

Article

Average D-distance Between Edges of a Graph

VIEWS 2080
PDF 492

Abstract
Full-Text HTML
Full-Text PDF
How to Cite

Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i2/58066

Year: 2015, Volume: 8, Issue: 2, Pages: 152–156

Original Article

Average D-distance Between Edges of a Graph

D. Reddy Babu^1* and P. L. N. Varma²

¹ Department of Mathematics, Koneru Lakshmaiah Education Foundation (K.L. University), Vaddeswaram, Guntur 522 502, India; reddybabu17@gmail.com

²Department of Science & Humanities, Vignan’s Foundation for Science, Technology and Research University, Vadlamudi, Guntur 522 213, India; varma_sh@vignanuniversity.org

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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