Menger’s theorem for m-polar fuzzy graphs and application of m-polar fuzzy edges to road network

Author:

Akram Muhammad1,Siddique Saba1,Ahmad Uzma1

Affiliation:

1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

Abstract

The main objective of this research article is to classify different types of m-polar fuzzy edges in an m-polar fuzzy graph by using the strength of connectedness between pairs of vertices. The identification of types of m-polar fuzzy edges, including α-strong m-polar fuzzy edges, β-strong m-polar fuzzy edges and δ-weak m-polar fuzzy edges proved to be very useful to completely determine the basic structure of m-polar fuzzy graph. We analyze types of m-polar fuzzy edges in strongest m-polar fuzzy path and m-polar fuzzy cycle. Further, we define various terms, including m-polar fuzzy cut-vertex, m-polar fuzzy bridge, strength reducing set of vertices and strength reducing set of edges. We highlight the difference between edge disjoint m-polar fuzzy path and internally disjoint m-polar fuzzy path from one vertex to another vertex in an m-polar fuzzy graph. We define strong size of an m-polar fuzzy graph. We then present the most celebrated result due to Karl Menger for m-polar fuzzy graphs and illustrate the vertex version of Menger’s theorem to find out the strongest m-polar fuzzy paths between affected and non-affected cities of a country due to an earthquake. Moreover, we discuss an application of types of m-polar fuzzy edges to determine traffic-accidental zones in a road network. Finally, a comparative analysis of our research work with existing techniques is presented to prove its applicability and effectiveness.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

Reference32 articles.

1. m-polar fuzzy labeling graphs with application;Akram;Mathematics in Computer Science,2016

2. Akram M. , Akmal R. , Alshehri N. , On m-polar fuzzy graph structures, 5 (2016), 1448 (19 pages).

3. Certain metrices in m-polar fuzzy graphs;Akram;New Mathematics and Natural Computation,2016

4. Certain types of edge m-polar fuzzy graphs;Akram;Iranian Journal of Fuzzy Systems,2017

5. Novel applications of m-polar fuzzy hypergraphs;Akram;Journal of Intelligent and Fuzzy Systems,2017

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