A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most on...

In any graph G = (V,E) that is not necessarily finite, a graphoidal cover is a set ψ of nontrivial paths P1, P2, . . . , not necessarily open and called ψ -edges, such that (GC-1) no vertex of G is an internal vertex of more than one path in ψ, and (GC-2) every edge of G is in exactly one of the paths in ψ. A ψ -dominating set of G is then defined as a set D of vertices in G such that every ver...

0

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