Connectedness in Soft Semigraphs

Abstract

Soft set theory is a general mathematical method for dealing with uncertain data. It is a classification of elements of the universe with respect to some given set of parameters. Semigraph is a generalization of graph which is different from hypergraph. Soft semigraph was introduced by applying the concept of soft set in semigraph. Connectedness is one of the basic concepts of graph theory. In this paper, we introduce the concepts of [Formula: see text]-walk, [Formula: see text]-trail, [Formula: see text]-path and [Formula: see text]-cycle in soft semigraphs and we define an [Formula: see text]-connected soft semigraph. We explain the procedures of vertex and [Formula: see text]-edge deletions from a soft semigraph. Also, we introduce [Formula: see text]-part cut vertex, [Formula: see text]-cut vertex, [Formula: see text]-part bridge and [Formula: see text]-bridge of a soft semigraph and investigate some of their properties.