Maximal Product of Graphs under Vague Environment

Behnaz Sheikh Hoseini,Muhammad Akram,Hossein Rashmanlou,Rajab Ali Borzooei,Mehrnaz Sheikh Hosseini

doi:10.3390/mca25010010

Behnaz Sheikh Hoseini, Muhammad Akram + Show 3 more

Open Access

https://doi.org/10.3390/mca25010010

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Abstract

Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we present a new product of graphs, namely, maximal product of two vague graphs. Then we describe certain concepts, including strongly, completely, regularity and connectedness on a maximal product of vague graphs. Further, we consider some results of edge regular and totally edge regular in a maximal product of vague graphs. Finally, we present an application for optimization of the biomass based on a maximal product of vague graphs.

Highlights

In the real world, there are data values that are uncertainly specified in many applications, for instance sensor information
A vague set introduced by Gau and Buehrer [3] is a further extension of a fuzzy set
Instead of using point-based membership as in fuzzy set, interval-based membership is used in a vague set and to describe the boundaries of the membership degree, a true-membership function and a false membership function are used

Summary

Introduction

There are data values that are uncertainly specified in many applications, for instance sensor information. The fuzzy set theory [1] has been introduced to handle this vagueness by extending the concept of belonging to a set. Many researchers discussed the graph theoretical concepts in generalized fuzzy environment, such as Pythagorean fuzzy graphs (PFG) [15], complex Pythagorean fuzzy graphs [16], rough fuzzy graphs [17] and q-rung orthopair fuzzy graphs [18] along with its decision making applications. Many scholars discussed product operations on various generalized fuzzy graphs. Mordeson and Peng [19] defined some of these product operations on fuzzy graphs. Utilizing these operations, the degree of the vertices is obtained from two fuzzy graphs in Reference [20]. We present an application for optimization of the biomass based on maximal product of vague graphs

Maximal Products of Vague Graphs

Application

Conclusions