Abstract
Suppose Γ is a finite simple graph. If D is a dominating set of Γ such that each is contained in the set of vertices of an odd cycle of Γ, then we say that D is an odd dominating set for Γ. For a finite group G, let denote the character graph built on the set of degrees of the irreducible complex characters of G. In this paper, we show that the complement of contains an odd dominating set, if and only if is a disconnected graph with non-bipartite complement.
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