Soft Semigraphs and Different Types of Degrees, Graphs and Matrices Associated with Them

Discrete and Computational Geometry, Graphs, and Games

Abstract

This is an introductory paper on soft semigraphs. Semigraph is a generalization of graph introduced by E. Sampathkumar which is different from hypergraph. In 1999, D. Molodtsov initiated the novel concept of soft set theory. This is an approach for modelling vagueness and uncertainty. It is a classification of elements of the universe with respect to some given set of parameters. The concept of soft graph introduced by Rajesh K. Thumbakara and Bobin George is used to provide a parameterized point of view for graphs. The theory of soft graphs is a fast developing area in graph theory due to its capability to deal with the parameterization tool. In this paper, we introduce soft semigraph by applying the concept of soft set in semigraph. Also, we introduce different types of degrees, graphs and matrices associated with a soft semigraph and investigate some of their properties.