Abstract: 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
graphoidal covering number of G and is denoted by ηia(G) or ηia.
Here we find induced acyclic graphoidal cover for some classes of
graphs.
Abstract: An induced graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least 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 cycle or an induced path. The minimum cardinality of an induced graphoidal cover of G is called the induced graphoidal covering number of G and is denoted by ηi(G) or ηi. Here we find induced graphoidal cover for some classes of graphs.