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

Some Edge Domination Parameters in Bipolar Hesitancy fuzzy graph

In this article, we establish edge domination in Bipolar Hesitancy Fuzzy Graph(BHFG). Various domination parameters such as inverse edge domination and total edge domination in BHFG are determined. Some theorems related to edge domination and examples are also discusse

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

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

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

The hub number of a fuzzy graph

In this paper, we introduced the concepts of hub number in fuzzy graph and is denoted by h(G). The hub number of fuzzy graph G is the minimum fuzzy cardinality among all minimal fuzzy hub sets . We determine the hub number h(G) for several classes of fuzzy graph and obtain Nordhaus-Gaddum type results for this parameter. Further, some bounds of h(G) are investigated. Also the relations between h(G) and other known parameters in fuzzy graphs are investigated.Publisher's Versio