V N Srinivasa rao Repalle

Objective A single valued neutrosophic set represented the uncertainty of real life situations in terms of membership $$(t)$$ ( t ) , indeterminacy $$(i)$$ ( i ) and non-membership $$(f)$$ ( f ) degree. However, this uncertainty cannot be limited to those three degrees; there is also an additional refusal degree. For this issue, the Turiyam set is an appropriate tool, which described the neutrosophic refusal degree of this situation as a liberal $$(l)$$ ( l ) degree in addition to those three degrees. The graphical representation of this situation is required for knowledge processing. For this purpose, the Turiyam graph was introduced as an extension of the single valued neutrosophic graph. This graph is helpful when the depictions of the vertices or their relationships or both, are considered in terms of membership $$(t)$$ ( t ) , indeterminacy $$(i)$$ ( i ) , non-membership $$(f)$$ ( f ) and liberal $$(l)$$ ( l ) degrees. The goal of this paper is to introduce the degree, order an...

Objective The study of total fuzzy graphs in all cases is crucial for the development of both theories and applications of the graph theory. Without theory the application will not be developed. Hence this manuscript attempted to theorize the conception of partially total fuzzy graphs. Results The article introduced the partially total fuzzy graph by keeping all the conditions of fuzziness as it is. From these definitions, it is endeavored to get the partial total fuzzy graph of a given fuzzy graph which is supported by illustrations. Also, some propositions and theorems related to this concept were developed and proved.

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 the strong fuzzy chromatic number for fuzzy graphs & related through 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 number for the fuzzy graphs are obtained. Mathematics Subject Classification: 05C72; 05C15; 05C31.

Objectives The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models. A bipolar fuzzy graph(BFG) provides more flexibility while modeling human thinking as compared with a fuzzy graph, and an interval valued bipolar fuzzy graph(IVBFG) has numerous applications where the real-life problem are time dependent and there is a network structure complexity. The aim of this paper is to introduce an interval-valued bipolar line fuzzy graph(IVBFLG). Result In this paper, we have proposed the notion of an IVBFLG and some of its characterizations. Also, some propositions and theorems related to an IVIFLGs are developed and proved. Furthermore, isomorphism between two IVIFLGs toward their IVIFGs was determined and verified. As a result, we derive a necessary and sufficient condition for an IVBFG to be isomorphic to its corresponding I...

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.

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on α-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results 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.

This document is devoted to the notion of annihilators of Pre A*-algebra. The concept of annihilator ideal is originated in a Pre A*-algebra and acknowledged varied characteristics. It is established a Hayting algebra from the ideals of a Pre A*algebra. An equivalent circumstance for a prime ideal of a Pre A*-algebra to stand minimal is accomplished. Equivalent conditions for a Spectrum of a Pre A*-algebra to be a T_1 – space are documented.

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on í µí»¼-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.