Simple Acyclic Graphoidal Covering Number In A Semigraph

Simple acyclic graphoidal covers in a graph

On 2-graphoidal Covering Number of a Graph

A 2-graphoidal cover of a graph G is a collection ψ of paths (not necessarily open) in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most two paths in ψ and every edge of G is in exactly one path in ψ. The minimum cardinality of a 2-graphoidal cover of G is called the 2-graphoidal covering number of G and is denoted by η2(G) or η2. Here, we...

The Monophonic Graphoidal Covering Number of a Graph

Abstract: 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 monophonic graphoidal cover of a graph G is a collection ψm of monophonic paths in G such that every vertex of G is an internal vertex of at most one monophonic path in ψm and every edge of G is in exactly one monophonic path in ψm. The minimum card...

Induced Acyclic Graphoidal Covers in a Graph

An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoida...

on label graphoidal covering number-i

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...