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.
Topological indices (TIs) are functional tools which correlate with a computational value through a undirected, finite and simple networks. Many physicochemical properties and chemical reactions are studied with the help of these TIs. Recently, they are commonly used in the behavior of quantitative structures activity as well as property relationships. In 1972, connection number based TIs are studied by Gutman and Trinajstić to calculate the entire π-electron energy of the alternant hydrocarbons. Moreover, the data provided by the website http://www.moleculardescriptors.eu shows that the relations between Zagreb indices and connection based indices that provide the better absolute values of the correlation coefficients for the thirteen physicochemical properties of the octane isomers. In this paper, we discuss the two invariants which are modified indices and modified coindices based on connection number of the resultant networks obtained by the different operations of product such as lexicographic and corona. For the molecular networks such as fence, closed fence, alkene and cycloalkane are depicted in the consequences of the obtained results. The comparisons between two invariants of the aforemention molecular networks are also presented through tables and graphical depictions. In addition, the uses and significance related to product of networks are also included. "INDEX TERMS "Indices and coindices; Product of networks; Connection number."
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