Cubic graphs and their application to a traffic flow problem

Abstract

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we introduce the concept of cubic graph, which is different from the notion of cubic graph in S. Rashid, N. Yaqoob, M. Akram, M. Gulistan, Cubic graphs with application, Int. J. Anal. Appl. 16 (2018), 733–750, and investigate some of their interesting properties. Then we define the notions of cubic path, cubic cycle, cubic diameter, strength of cubic graph, complete cubic graph, strong cubic graph and illustrate these notions by several examples. We prove that any cubic bridge is strong and we investigate equivalent condition for cubic cutvertex. Finally, we use the concept of cubic graphs in traffic flows to get the least time to reach the destination.