Simple Acyclic Graphoidal Covering Number In A Semigraph

Abstract

A simple graphoidal cover of a semigraph  is a graphoidal cover  of  such that any two paths in  have atmost one end vertex in common. The minimum cardinality of a simple graphoidal cover of  is called the simple graphoidal covering number of a semigraph and is denoted by . A simple acyclic graphoidal cover of a semigraph  is an acyclic graphoidal cover  of  such that any two paths in  have atmost one end vertex in common. The minimum cardinality of a simple acyclic graphoidal cover of  is called the simple acyclic graphoidal covering number of a semigraph and is denoted by . In this paper we find the simple acyclic graphoidal covering number for wheel in a semigraph, unicycle in a semigraph and zero-divisor graph.