Abstract
For a finite group G, let Δ(G) denote the character graph built on the set of degrees of the irreducible complex characters of G. In this article, we determine the structure of all finite groups G with K4-free character graph Δ(G) having seven vertices. We also obtain a classification of all K4-free graphs with seven vertices which can occur as character graphs of some finite groups.
Acknowledgments
I would like to express my gratitude to the referee for valuable comments which improved the original version. I also would like to thank Sadegh Nazardonyavi for his help during the preparation of the manuscript.