DOIAbstract
A graphoidal cover of a graph G (not necessarily finite) is a collection ψ of paths in G, called ψ-edges, (not necessarily finite, not necessarily open) satisfying the following axioms: (GC-1) Every vertex of G is an internal vertex of at most one path in ψ, and (GC-2) every edge of G is in exactly one path in ψ. The pair is called a graphoidally covered graph. In a graphoidally covered graph two distinct vertices u and v of G are ψ-adjacent if they are the ends of a finite open path in ψ. A graphoidally covered graph (or G) in which no two distinct vertices are ψ-adjacent is called ψ-independent and a graph G possessing a graphoidal cover ψ such that G is ψ-independent is called a graphoidally independent graph. This paper is an attempt to...
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