The neutrosophic quadripartitioned soft model is a hybrid model by combining neutrosophic soft sets with quadripartitioned sets. This work concerns with the quadripartitioned neutrosophic soft graphs for treating neutrosophic soft information by employing the theory of quadripartitioned neutrosophic soft sets with graphs. Operations like Cartesian product, cross product, lexicographic product, and strong product of quadripartitioned neutrosophic soft graphs are established. The proposed concepts are explained with examples.
Top1 Introduction
The author Zadeh in 1975 invented the interval-valued fuzzy sets as the generalisation of fuzzy sets (Zadeh, 1975). To handle the uncertainty, it utilizes the values of intervals of numbers instead of numbers as the membership function. To reflect the grade of membership of fuzzy set A [TAL(x), TAU(x)] with 0≤TAL(x), TAU(x)≤1 is widely employed (Turksen, 1986). It is crucial to use interval-valued fuzzy sets in applications such as fuzzy control. The indeterminacy portion of the neutrosophic set is divided into two parts: ‘Contradiction’ (both true and false) and ‘Unknown’ (neither true nor false), that is 
and 
which defines a new set called ‘quadripartitioned single valued neutrosophic set’, introduced by (Chatterjee, 2016). This study is completely based on “Belnap’s four valued logic” (Belnap, 1977) and Smarandache’s “Four Numerical valued neutrosophic logic” (Smarandache, 2014). The efficiency of neutrosophic sets in holding incomplete data and handling uncertain information is the foundation for their current success in modelling natural occurrences. It is the base of neutrosophic logic, a multiple value logic that generalizes the fuzzy logic that carries with paradoxes, contradictions, antitheses, antinomies, invented by the author Smarandache in (Smarandache, 2014; Smarandache, 1999; Smarandache, 2010). The single-valued neutrosophic set is the generalization of intuitionistic fuzzy sets and is used expediently to deal with real-world problems, especially in decision support (Wang, 2010). The computation of belief in that element (truth), they disbelieve in that element (falsehood) and the indeterminacy part of that element with the sum of these three components are strictly less than 1. Neutrosophic set and related notions have shown applications in many different fields. In the definition of neutrosophic set, the indeterminacy value is quantified explicitly and truth-membership, indeterminacy membership, and false-membership are defined completely independent with the sum of these values lies between 0 and 3 (Smarandache, 1998; Smarandache, 2010; Turksen 1986).
Thus, a single-valued neutrosophic set is a powerful general formal framework which generalizes the concept of fuzzy set and intuitionistic fuzzy set. Group decision-making is a commonly used tool in human activities, which determines the optimal alternative from a given finite set of alternatives using the evaluation information given by a group of decision-makers or experts. With the rapid development of society, group decision-making plays an increasingly important role when dealing with the decision-making problems