New Concepts of Vertex Covering in Cubic Graphs with Its Applications

Huiqin Jiang, Ali Asghar Talebi, Zehui Shao, Seyed Hossein Sadati and Hossein Rashmanlou
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Huiqin Jiang: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Ali Asghar Talebi: Department of Mathematics, University of Mazandaran, 4741613534 Babolsar, Iran
Zehui Shao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Seyed Hossein Sadati: Department of Mathematics, University of Mazandaran, 4741613534 Babolsar, Iran
Hossein Rashmanlou: Department of Mathematics, University of Mazandaran, 4741613534 Babolsar, Iran

Mathematics, 2022, vol. 10, issue 3, 1-29

Abstract: Graphs serve as one of the main tools for the mathematical modeling of various human problems. Fuzzy graphs have the ability to solve uncertain and ambiguous problems. The cubic graph, which has recently gained a position in the fuzzy graph family, has shown good capabilities when faced with problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Simultaneous application of fuzzy and interval-valued fuzzy membership indicates a high flexibility in modeling uncertainty issues. The vertex cover is a fundamental issue in graph theory that has wide application in the real world. The previous definition limitations in the vertex covering of fuzzy graphs has directed us to offer new classifications in terms of cubic graph. In this study, we introduced the strong vertex covering and independent vertex covering in a cubic graph with strong edges and described some of its properties. One of the motives of this research was to examine the changes in the strong vertex covering number of a cubic graph if one vertex is omitted. This issue can play a decisive role in covering the graph vertices. Since many of the problems ahead are of hybrid type, by reviewing some operations on the cubic graph we were able to determine the strong vertex covering number on the most important cubic product operations. Finally, two applications of strong vertex covering and strong vertex independence are presented.

Keywords: cubic graph; cubic strong edge; strong vertex covering number; strong vertex independent set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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