Properties of edge-deleted distance stable graphs

✍ Scribed by Klemm, Karen; Winters, Steven J.

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 72 KB
• Volume: 34
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/(sici)1097-0037(199912)34:4<279::aid-net7>3.0.co;2-p

✦ Synopsis

The distance from a vertex u to a vertex v in a connected graph G is the length of a shortest u-v path in G. The distance of a vertex v of G is the sum of the distances from v to the vertices of G. For a vertex v in a 2-edge-connected graph G, we define the edge-deleted distance of v as the maximum distance of v in G Ϫ e over all edges e of G. A vertex is an edge-deleted distance stable vertex if the difference between its edge-deleted distance and distance is 1. A 2-edge-connected graph G is an edge-deleted distance stable graph if each vertex of G is an edge-deleted distance stable vertex. In this paper, we investigate the edge-deleted distance of vertices and describe properties of edge-deleted distance stable graphs.