Abstract
The competition graph is a well-studied topic. But, the fuzzy competition graph has been defined recently and investigated many properties. Only one component is considered for every vertex and edge in a fuzzy competition graph. In an interval-valued m-polar fuzzy graph, each vertex and each edge have m number of membership values, all of which are intervals in [0, 1]. So, defining a competition graph for an interval-valued m-polar fuzzy graph is not easy and needs some new ideas. By considering m interval-valued components of the membership value of a vertex or edge, interval-valued m-polar fuzzy competition graph (IVmPFCG) has been defined. Many interesting properties are presented on IVmPFCG. Here, two more generalizations of IVmPF competition graph, namely interval-valued m-polar fuzzy k-competition graph (IVmPFkCG) and interval-valued m-polar fuzzy p-competition graph (IVmPFkCG) are introduced and studied some of their interesting properties. These graphs are directly related to directed IVmPFG. Based on open and closed neighborhoods of vertices, different types of neighborhood graphs are defined and studied for some of their intersecting properties. Also, another type of competition graph, namely q-step interval-valued m-polar fuzzy competition graph, is introduced and investigated some of its exciting properties thoroughly. Lastly, a real-life application based on an interval-valued m-polar fuzzy competition graph has been discussed.
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Mahapatra, T., Ghorai, G. & Pal, M. Competition graphs under interval-valued m-polar fuzzy environment and its application. Comp. Appl. Math. 41, 285 (2022). https://doi.org/10.1007/s40314-022-01987-z
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DOI: https://doi.org/10.1007/s40314-022-01987-z