A note on fractional ID-[a,b]-factor-critical covered graphs

• Published in: Discrete Applied Mathematics Vol. 319; pp. 511 - 516
• Main Authors: Zhou, Sizhong, Liu, Hongxia, Xu, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.10.2022
• Subjects: Fractional [formula omitted]-factor; Fractional ID-[formula omitted]-factor-critical covered graph; Graph; Minimum degree; Neighborhood; Fractional [a,b]-factor; Graph; Minimum degree; Fractional ID-[a,b]-factor-critical covered graph; Neighborhood
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2021.03.004

In communication networks, the existence of fractional factors can be characterized as the feasibility of data transmission. When some nonadjacent nodes with each other are damaged and a special channel is assigned, the possibility of data transmission in a communication network is equivalent to the existence of fractional ID-factor-critical covered graph. As a consequence, the existence of fractional ID-[a,b]-factor-critical covered graph plays a key role in studying data transmissions of communication networks. Neighborhood and minimum degree of a graph or a network are often used to measure the vulnerability and robustness of a graph or a network, which are two important parameters considered in network design. In this article, we mainly investigate the relationship between neighborhood of independent set, minimum degree and the fractional ID-[a,b]-factor-critical covered graph, and acquire a neighborhood of independent set and minimum degree condition for a graph being fractional ID-[a,b]-factor-critical covered, which is a generalization of the previous results.