AN STUDY ON FUZZY COLORING APPROACH

The field of Maths assumes an indispensable job in different fields.Graph theory is asignificant zonein Maths, utilized for several models. An old style graph speaks to an old style connection among objects. The items are spoken to by vertices & relations by edges. Coloring of Graph is a considered issue of combinatorial streamlining. Theory of F-graphs has various applications in current science & innovation, particularly in neural networksfields, information theory, cluster analysis, expert systems, control theory, medical diagnosis, etc. In 1975Rosenfeldpresented the concept of F-graphs. The coloring of F-graphshas a few applications in reality. Graph coloring fills in as a model for compromise in issues of combinatorial improvement. F-graphsColoring has some genuine combinatorial streamlining applications issues as exam schedule, allocation registration, systemof traffic light, and so forth. The most significant issue in the coloring issue of the F-graphis to develop a strategy for finding F-graphschromatic numbers. In this Article, we analyzed Coloring Approach in Fuzzy Graph Theory

Some properties of vague graph structures

A graph structure is a generalization of simple graphs. Graph structures are very useful tools for the study of different domains of computational intelligence and computer science. A vague graph structure is a generalization of a vague graph. In this research paper, we present several different types of operations including cartesian product, cross product, lexicographic product, union, and composition on vague graph structures. We also introduce some results of operations.Publisher's Versio

A study on irregularity in vague graphs with application in social relations

Considering all physical, biological and social systems, fuzzy graph models serves the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problems, which are mostly uncertain, modelling those problems based on fuzzy graph is highly demanding for an expert. Vague graph can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which fuzzy graphs possibly will not succeed into bringing about satisfactory results. Also, vague graphs are so useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, and traffic plan. Hence, in this paper, we introduce strongly edge irregular vague graphs and strongly edge totally irregular vague graphs. A comparative study between strongly edge irregular vague graphs and strongly edge totally irregular vague graphs is done. Finally, we represent an applicationof irregular vague influence graph to show the importance of irregularity in vague graphs.Publisher's Versio

Bipolar fuzzy graphs based on the product operator

From both theoretical and experimental perspectives, bipolar fuzzy set theory serves as a foundation for bipolar cognitive modeling and multi-agent decision analysis, where the product operator may be preferred over the min operator in some scenarios. In this paper, we discuss the basic properties of operations on product bipolar fuzzy graphs (PBFGs)(bipolar fuzzy graphs based on the product operator) such as direct product, Cartesian product, strong product, lexicographic product, union, ring sum and join. Also we define the notion of complement of PBFGs and investigate its properties. Moreover, application of PBFG theory is presented in multi-agent decision making.Publisher's Versio

Novel concepts in vague incidence graphs with application

Fuzzy graph (FG) models enjoy the ubiquity of being in natural and humanmade structures, namely dynamic process in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems, which are often uncertain, it is highly difficult for an expert to model those problems based on an FG. Vague incidence graph (VIG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem, where FGs may fail to reveal satisfactory results. Also, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, capturing the image, and also other issues such as medical sciences, and traffic planning. Hence, in this research, we introduce new operations on VIGs, namely, maximal product, rejection, and residue product with several examples. Likewise, some results related to operations have been described.Publisher's Versio

Some properties of m-polar fuzzy graphs

AbstractIn many real world problems, data sometimes comes from n agents (n ≥ 2), i.e., “multipolar information” exists. This information cannot be well-represented by means of fuzzy graphs or bipolar fuzzy graphs. Therefore, m-polar fuzzy set theory is applied to graphs to describe the relationships among several individuals. In this paper, some operations are defined to formulate these graphs. Some properties of strong m-polar fuzzy graphs, self-complementary m-polar fuzzy graphs and self-complementary strong m-polar fuzzy graphs are discussed

On some operations and density of m-polar fuzzy graphs

AbstractThe theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m-polar fuzzy graphs. It is proved that any of the products of m-polar fuzzy graphs are again an m-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m-polar fuzzy graphs is complete. If any of the products of two m-polar fuzzy graphs G1 and G2 are strong, then at least G1 or G2 must be strong. Moreover, the density of an m-polar fuzzy graph is defined, the notion of balanced m-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m-polar fuzzy graph is introduced, and it is shown that every product m-polar fuzzy graph is an m-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m-polar fuzzy graphs

A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the &mu -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here. Document type: Articl