Premium
All ( k ; g )‐cages are k ‐edge‐connected
Author(s) -
Lin Yuqing,
Miller Mirka,
Rodger Chris
Publication year - 2005
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20052
Subject(s) - combinatorics , mathematics , enhanced data rates for gsm evolution , graph , cage , girth (graph theory) , connectivity , discrete mathematics , computer science , telecommunications
A ( k ; g )‐cage is a k ‐regular graph with girth g and with the least possible number of vertices. In this paper, we prove that ( k ; g )‐cages are k ‐edge‐connected if g is even. Earlier, Wang, Xu, and Wang proved that ( k ; g )‐cages are k ‐edge‐connected if g is odd. Combining our results, we conclude that the ( k ; g )‐cages are k ‐edge‐connected. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 219–227, 2005