On Certain Products of Complex Intuitionistic Fuzzy Graphs

A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of real-life and physical events. Complex intuitionistic fuzzy graphs (CIFGs) are a broader type of diagram that may be used to manipulate data. In this paper, we define the key operations direct, semistrong, strong, and modular products for complex intuitionistic fuzzy graphs and look at some interesting findings. Further, the strong complex intuitionistic fuzzy graph is defined, and several significant findings are developed. Furthermore, we study the behavior of the degree of a vertex in the modular product of two complex intuitionistic fuzzy graphs.

Connectivity Indices of Intuitionistic Fuzzy Graphs and Their Applications in Internet Routing and Transport Network Flow

Connectivity index CI has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs IFGs allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of CI s in real life problems and comprehension of IFGs , we aim to develop some CI s in the environment of IFGs . We introduce two types of CI s , namely, CI and average CI , in the frame of IFGs . In spite of that, certain kinds of nodes called IF connectivity enhancing node IFCEN , IF connectivity reducing node IFCRN , and IF neutral node are introduced for IFGs . We have introduced strongest strong cycles, θ -evaluation of vertices, cycle connectivity, and CI of strong cycle. Applications of the CI s in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.

Complement of max product of intuitionistic fuzzy graphs

In this paper, the complement of max product of two intuitionistic fuzzy graphs is defined. The degree of a vertex in the complement of max product of intuitionistic fuzzy graph is studied. Some results on complement of max product of two regular intuitionistic fuzzy graphs are stated and proved. Finally, we provide an application of intuitionistic fuzzy graphs in school determination using normalized Hamming distance.

Graphical Structures of Cubic Intuitionistic Fuzzy Information

The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such as the idea subgraphs, degree of CIFG, order of CIFG, complement of CIFG, path in CIFG, strong CIFG, and the concept of bridges for CIFGs. Furthermore, the generalization of CIFG is proved with the help of some remarks. In addition, the comparison among the existing and the proposed ideas is carried out. Finally, an application of CIFG in decision-making problem is studied, and some future study is proposed.

Graphical Analysis of Covering and Paired Domination in the Environment of Neutrosophic Information

Neutrosophic graph (NG) is a powerful tool in graph theory, which is capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) may not handle these problems as efficiently as NGs. It is difficult to model uncertainty due to imprecise information and vagueness in real-world scenarios. Many real-life optimization problems are modeled and solved using the well-known fuzzy graph theory. The concepts of covering, matching, and paired domination play a major role in theoretical and applied neutrosophic environments of graph theory. Henceforth, the current study covers this void by introducing the notions of covering, matching, and paired domination in single-valued neutrosophic graph (SVNG) using the strong edges. Also, many attention-grabbing properties of these concepts are studied. Moreover, the strong covering number, strong matching number, and the strong paired domination number of complete SVNG, complete single-valued neutrosophic cycle (SVNC), and complete bipartite SVNG are worked out along with their fascinating properties.

A Study on Connectivity Concepts in Intuitionistic Fuzzy Graphs

In this paper, we introduced some concepts of connectivity in an intuitionistic fuzzy graphs, also we study intuitionistic fuzzy cut vertices and intuitionistic fuzzy bridges in fuzzy graph. Connectivity in complete intuitionistic fuzzy graphs is also studied