A Note of Generalization of Fractional ID-factor-critical Graphs

Article type: Research Article

Authors: Zhou, Sizhong^{; *}

Affiliations: School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, China. zsz_cumt@163.com

Correspondence: [*] Address of correspondence: School of Science, Jiangsu University of Science and Technology, Changhui Road 666, Zhenjiang, Jiangsu 212100, China.

Abstract: In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional ID-[a, b]-factor-critical covered graphs have a great deal of important applications in the data transmission networks. In this paper, we investigate the relationship between the binding numbers of graphs and the fractional ID-[a, b]-factor-critical covered graphs, and derive a binding number condition for a graph to be fractional ID-[a, b]-factor-critical covered, which is an extension of Zhou’s previous result [S. Zhou, Binding numbers for fractional ID-k-factor-critical graphs, Acta Mathematica Sinica, English Series 30(1)(2014)181–186].

Keywords: network, graph, binding number, fractional [a, b]-factor, fractional ID-[a, b]-factor-critical covered graph

DOI: 10.3233/FI-222130

Journal: Fundamenta Informaticae, vol. 187, no. 1, pp. 61-69, 2022