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The Scientific World Journal
Volume 2014, Article ID 369798, 7 pages
Research Article

Toughness Condition for a Graph to Be a Fractional -Critical Deleted Graph

1School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
2Editorial Department of Yunnan Normal University, Kunming 650092, China

Received 16 January 2014; Revised 21 June 2014; Accepted 21 June 2014; Published 9 July 2014

Academic Editor: Abdelalim A. Elsadany

Copyright © 2014 Wei Gao and Yun Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A graph is called a fractional -deleted graph if admits a fractional -factor for any . A graph is called a fractional -critical deleted graph if, after deleting any vertices from , the resulting graph is still a fractional -deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received significant attention in computer science. In this paper, we present the relationship between toughness and fractional -critical deleted graphs. It is determined that is fractional -critical deleted if .