An approximation of balanced score in neutrosophic graphs with weak edge weights

Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridge-lifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented

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

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

Interval- valued fermatean neutrosophic graphs

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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

Nidus idearum. Scilogs, III: Viva la Neutrosophia!

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas! * Neutrosophy is a new branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. I coined the words “neutrosophy” and “neutrosophic” in my 1998 book: Florentin Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf (last edition online)

Concepts of vertex regularity in cubic fuzzy graph structures with an application

The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and fuzzy graph structures, shows better capabilities in solving complex problems, especially in cases where there are multiple relationships. The quality and method of determining the degree of vertices in this type of fuzzy graphs simultaneously supports fuzzy membership and interval-valued fuzzy membership, in addition to the multiplicity of relations, motivated us to conduct a study on the regularity of cubic fuzzy graph structures. In this context, the concepts of vertex regularity and total vertex regularity have been informed and some of its properties have been studied. In this regard, a comparative study between vertex regular and total vertex regular cubic fuzzy graph structure has been carried out and the necessary and sufficient conditions have been provided. These degrees can be easily compared in the form of a cubic number expressed. It has been found that the condition of the membership function is effective in the quality of degree calculation. In the end, an application of the degree of vertices in the cubic fuzzy graph structure is presented

Isolated Single Valued Neutrosophic Graphs

Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph