Connectivity indices of m-polar fuzzy network model, with an application to a product manufacturing problem

Abstract

Connectivity is among the most essential concerns in graph theory and its applications. We consider this issue in a framework that stems from the combination of m-polar fuzzy set theory with graphs. We introduce two measurements of connectedness of m-polar fuzzy graphs that we call their connectivity and average connectivity indices. Examples are given, and the theoretical performance of these concepts is investigated. Particularly, we are concerned with the effect of deleting a vertex or an edge from an m-polar fuzzy graph, on its connectivity and average connectivity indices. We also establish bounding expressions for the connectivity index in complete m-polar fuzzy graphs, complete bipartite m-polar fuzzy graphs, and wheel m-polar fuzzy graphs. Moreover, we introduce some special types of vertices called m-polar fuzzy connectivity reducing vertices, m-polar fuzzy connectivity enhancing vertices, and m-polar fuzzy connectivity neutral vertices. Our theoretical contribution is applied to a product manufacturing problem that takes advantage of multi-polar uncertain information. The justification for our application is systematized using an algorithm. Finally, we compare the proposed method to existing methodologies to demonstrate its feasibility and applicability.

Keywords: Average connectivity index; Connectivity index; Special types of vertices.; m-Polar fuzzy graphs.