Representation of graphs based on neighborhoods and soft sets

Abstract

Neighborhood of each vertex in a graph can be very useful in its representation. Soft set theory provides a new tool for such representation. In this paper, a method is being introduced for a graph representation, which is based on adjacency of vertices and soft set theory. With this representation of a graph, application of algebraic operations, available in soft sets may reveal many new aspects of graph theory. In addition, a metric is defined to find distances between graphs represented by soft sets.