Objective
Recently, the Turiyam set was introduced as an extension of the neutrosophic set to handle the uncertainty data set beyond its truth, indeterminacy and falsity values. This article introduced the Cartesian product of Turiyam sets and Turiyam relations. Further, we defined operations on Turiyam relations as well as discussed the inverse and types of Turiyam relations.
Results
The Cartesian product of Turiyam sets, Turiyam relations, inverse Turiyam relation and types of Turiyam relations are stated and their properties are derived. Furthermore, examples are given to clarify some concepts.
Objectives
In the field of graph theory, an intuitionistic fuzzy set becomes a useful tool to handle problems related to uncertainty and impreciseness. We introduced the interval-valued intuitionistic fuzzy line graphs (IVIFLG) and explored the results related to IVIFLG.
Result
Some propositions and theorems related to IVIFLG are proposed and proved, which are originated from intuitionistic fuzzy graphs (IVIG). Furthermore, Isomorphism between two IVIFLGs toward their IVIFGs was determined and verified.
Objective
In the field of graph theory, maple is a technical computation form that is used for solving problems. In this article, we apply maple to find the strong fuzzy chromatic polynomial of fuzzy graphs and related. Moreover, we apply maple to obtain strong fuzzy chromatic numbers of fuzzy graphs using their strong fuzzy chromatic polynomials.
Results
The strong fuzzy chromatic polynomials for fuzzy graphs, strong fuzzy graphs and complete fuzzy graphs are determined using maple. Furthermore, the strong fuzzy chromatic numbers for the fuzzy graphs are obtained.
Coloring of fuzzy graphs has many real-life applications in combinatorial optimization problems like traffic light system, exam scheduling, and register allocation. The coloring of total fuzzy graphs and its applications are well studied. This manuscript discusses the description of 2-quasitotal graph for fuzzy graphs. The proposed concept of 2-quasitotal fuzzy graph is explicated by several numerical examples. Moreover, some theorems related to the properties of 2-quasitotal fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs and 1-quasitotal fuzzy graphs. Furthermore, it defines 2-quasitotal coloring of fuzzy total graphs and which is justified.
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