Abstract
For a finite group G G , let Δ ( G ) \Delta (G) denote the character graph built on the set of degrees of the irreducible complex characters of G G . In this paper, we show that if the diameter of Δ ( G ) \Delta (G) is equal to three, then the complement of Δ ( G ) \Delta (G) is bipartite. Also in this case, we determine the structure of the character graph Δ ( G ) \Delta (G) .
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