# On Edge-Distance and Edge-Eccentric Graph of a Graph Abstract views: 10 / PDF downloads: 9

## Authors

• Medha Itagi Huilgol Department of Mathematics, Bangalore University, Central College Campus, Bangalore, India
• S. Syed Asif Ulla Department of Mathematics, Bangalore University, Central College Campus, Bangalore, India

## Keywords:

Cycle, eccentric edge, edge - self centered graph, edge - distance degree regular graph, edge - eccentric graph

## Abstract

An elementary circuit (or tie) is a subgraph of a graph and the set of edges in this subgraph is called an elementary tieset. The distance $d(e_{i}, e_{j})$ between two edges in an undirected graph is defined as the minimum number of edges in a tieset containing $e_{i}$ and $e_{j}$. The eccentricity $\varepsilon_{\tau}(e_{i})$ of an edge $e_{i}$ is $\varepsilon_{\tau}(e_{i})=\displaystyle \max_{\substack{e_{j}\in E}}d(e_{i}, e_{j})$. In this paper, we have introduced the edge - self centered and edge - eccentric graph of a graph and have obtained results on these concepts.

15-09-2014

## How to Cite

Medha Itagi Huilgol, & S. Syed Asif Ulla. (2014). On Edge-Distance and Edge-Eccentric Graph of a Graph. International Journal of Mathematics And Its Applications, 2(3), 7–16. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/307

Research Article