New Bounds of Induced Acyclic Graphoidal Decomposition Number of a Graph
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An induced acyclic graphoidal decomposition (IAGD) of a graph G is a collection ψ of nontrivial induced paths in G such that every edge of G lies in exactly one path of ψ and no two paths in ψ have a common internal vertex. The minimum cardinality of an IAGD of G is called the induced acyclic graphoidal decomposition number denoted by ηia(G). In this paper we present bounds for ηia(G) in terms of cut vertices and simplicial vertices of G.
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