The authors in their work in [4] introduced a graph Γ(G,H), where G is a finite group and H is a subgroup of G such that the set of irreducible complex characters of G form the vertex set and two vertices χ and ψ are joined by an edge if their restriction to H, namelyχΗ and ψΗhave at least one irreducible character of H as a common constituent. In [8] M. Javarsineh and Ali Iranmanesh have studied the nature of this graph for the groupsD2n ,U6n and T4n. In this paper we study characterization properties of the graph Γ(G,H)and obtain various results relevant to this graph. This paper deals with several ideas and techniques used in representation theory and graph theory.
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