Sufficient conditions for the existence of fractional factors in different settings

被引：0

作者：

Gao, Wei ^{[1
]}

Shi, Ce ^{[2
]}

机构：

[1] School of Information Science and Technology, Yunnan Normal University, Kunming,650500, China

[2] School of Mathematics and Information Science, Shanghai Lixin University of Commerce, Shanghai,201620, China

来源：

IAENG International Journal of Applied Mathematics | 2019年 / 49卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Computer networks;

D O I：

暂无

中图分类号：

O144 [集合论]; O157 [组合数学（组合学）];

学科分类号：

070104 ;

摘要：

The fractional factor theory of graphs originated from the feasible flow problem in communication networks. With the development of computer networks, this problem has been highly valued by scholars from the field of computer science and mathematics. This paper studies the sufficient conditions for the existence of fractional factors in the different setting of network from a theoretical perspective. These theoretical results provide the basis for the initial network designing. We first study the relationship between vulnerable parameter in networks and the existence of fractional factor, and an isolated toughness condition for a graph to be fractional (g; f; n')-critical is determined. Then, we illustrate some neighborhood union conditions for independent-set-deletable deleted graphs, and point out that the conditions are best in some senses. Moreover, we present an independent set condition for a graph to be fractional ID-(g; f;m)-deleted. Also, the result is tight on independent set degree condition. Finally, we introduce the concept of all fractional ID-(g; f;m)-deleted graph, and several conclusions are obtained from the known results. © 2019, International Association of Engineers.

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