New concepts of domination in cubic graphs with application

Abstract

The cubic set, introduced as a combination of a fuzzy set and an interval-valued fuzzy set, provided researchers with more flexibility than the previous two sets in dealing with complex and uncertain problems. Fuzzy graphs, based on this type of set, are among the emerging fuzzy graphs that have a great potential to model the surrounding phenomena. Consistent with the special role that cubic graphs play in decision-making and selecting superior options, dominating these graphs is of great importance and value. In this paper, we introduce the domination of the cubic graphs in terms of strong edges and examine their properties. In addition, we examine domination in terms of independent sets and since many of the phenomena surrounding us are hybrid, we also discuss the domination concept on its fuzzy operations. Finally, we present an application of this graph on the subject of domination.