A STUDY ON DISTANCE OF FUZZY GRAPH THEORY

Graph theory is one of the parts of current Mathshaving encountered a most noteworthy advancement lately. The theory of fuzzy graphs was created by in the year 1975. During a similarand have additionally presented different connectedness ideas in fuzzy graphs. Fuzzy set theory gives us not just an important and ground-breaking portrayal of measurement of vulnerabilities, yet an increasingly reasonable portrayal of dubious ideas communicated in natural languages. A few properties of unusual hubs, fringe hubs and focal hubs are gotten. The scientific implanting of ordinary set theory into fuzzy has become a natural marvel. Therefore the possibility of fluffiness is an improving one. This Research study analyzes the distancetotal conceptthat is a measurement, in a fuzzy graph is presented

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

Contraction and domination in fuzzy graphs

Fuzzy sets and logics is a true crowning achievement of the century. Among the variety of exemplary changes in science and technology, the concept of uncertainty played a significant role, which led to the development of fuzzy sets, which in turn helped in the transition from graph theory to fuzzy graph theory. This paper familiarizes an improved concept in fuzzy graphs, called contraction. Two types of contraction namely edge contraction and neighbourhood contraction are introduced. We developed these two concepts in fuzzy graphs and analyse its effect on domination number and edge domination number. Any research is meaningful only by its contribution to the society. The modern world and the field of networks are inseparable. We have applied our concept to a wired network problem.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

Cyclic Symmetry of Riemann Tensor in Fuzzy Graph Theory

In this paper, we define a graph-theoretic analog for the Riemann tensor and analyze properties of the cyclic symmetry. We have developed a fuzzy graph-theoretic analog of the Riemann tensor and have analyzed its properties. We have also shown how the fuzzy analog satisfies the properties of the 6X6 matrix of the Riemann tensor by expressing it as a union of the fuzzy complete graph formed by the permuting vertex set and a Levi-Civita graph analog. We have concluded the paper with a brief discussion on the similarities between the properties of the fuzzy graphical analog and the Riemann tensor and how it can be a plausible analogous model for the Petrov-Penrose classification.Comment: 12 pages, 1 figur

Strong Domination Index in Fuzzy Graphs

Topological indices play a vital role in the area of graph theory and fuzzy graph (FG) theory. It has wide applications in the areas such as chemical graph theory, mathematical chemistry, etc. Topological indices produce a numerical parameter associated with a graph. Numerous topological indices are studied due to its applications in various fields. In this article a novel idea of domination index in a FG is defined using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of a FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle and fuzzy stars. Inequalities involving the SDD and SDI are obtained. The union and join of FG is also considered in the study. Applications for SDD of a vertex is provided in later sections. An algorithm to obtain a MSDS containing a particular vertex is also discussed in the article

Study on a strong and weak n-connected total perfect k-dominating set in fuzzy graphs

In this paper, the concept of a strong n-Connected Total Perfect k-connected total perfect k-dominating set and a weak n-connected total perfect k-dominating set in fuzzy graphs is introduced. In the current work, the triple-connected total perfect dominating set is modified to an n-connected total perfect k-dominating set n(ctpkD)(G) and number gamma n(ctpkD)(G). New definitions are compared with old ones. Strong and weak n-connected total perfect k-dominating set and number of fuzzy graphs are obtained. The results of those fuzzy sets are discussed with the definitions of spanning fuzzy graphs, strong and weak arcs, dominating sets, perfect dominating sets, generalization of triple-connected total perfect dominating sets of fuzzy graphs, complete, connected, bipartite, cut node, tree, bridge and some other new notions of fuzzy graphs which are analyzed with a strong and weak n(ctpkD)(G) set of fuzzy graphs. The order and size of the strong and weak n(ctpkD)(G) fuzzy set are studied. Additionally, a few related theorems and statements are analyzed.Web of Science1017art. no. 317