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Properties of edge‐deleted distance stable graphs
Author(s) -
Klemm Karen,
Winters Steven J.
Publication year - 1999
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199912)34:4<279::aid-net7>3.0.co;2-p
Subject(s) - combinatorics , vertex (graph theory) , mathematics , neighbourhood (mathematics) , distance , graph , discrete mathematics , shortest path problem , mathematical analysis
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 − 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. © 1999 John Wiley & Sons, Inc. Networks 34: 279–282, 1999