Abstract
The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets overX(set of all vertices of a graph) andE(set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm.
Highlights
The correspondence between a vertex and its neighbors has an essential role in the structure of a graph
We describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm
Ali et al [16] presented some new operations in soft set theory and based on the analysis of several operations on soft sets Sezgin and Atagun [17] studied the theoretical aspect of the soft set theory
Summary
The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are based on the correspondence of primary parameters and underlying parameters. We present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets over X (set of all vertices of a graph) and E (set of all edges of a graph). We introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. We describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm
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