Gnanaseelan, T.; Selvaraj, C. Some characterization results on character graphs of groups. (English) Zbl 1310.20009 J. Appl. Math. Bioinform. 3, No. 2, 181-194 (2013). Summary: The authors in their work [in Int. J. Algebra 4, No. 9-12, 569-577 (2010; Zbl 1211.20010)] introduced a graph \(\Gamma(G,H)\), where \(G\) is a finite group and \(H\) is a subgroup of \(G\) such that the set of irreducible complex characters of \(G\) forms the vertex set and two vertices \(\chi\) and \(\psi\) are joined by an edge if their restrictions to \(H\), namely \(\chi_H\) and \(\psi_H\) have at least one irreducible character of \(H\) as a common constituent. In [Can. J. Sci. Eng. Math. 2, No. 5, 229-236 (2011)] M. Javarsineh and {ıA. Iranmanesh} have studied the nature of this graph for the groups \(D_{2n}\), \(U_{6n}\) and \(T_{4n}\). In this paper we study characterization properties of the graph \(\Gamma(G,H)\) and obtain various results relevant to this graph. This paper deals with several ideas and techniques used in representation theory and graph theory. MSC: 20C15 Ordinary representations and characters 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20C20 Modular representations and characters 05E10 Combinatorial aspects of representation theory Keywords:relative character graphs; irreducible complex characters; character restrictions; normal products of graphs Citations:Zbl 1211.20010 PDFBibTeX XMLCite \textit{T. Gnanaseelan} and \textit{C. Selvaraj}, J. Appl. Math. Bioinform. 3, No. 2, 181--194 (2013; Zbl 1310.20009)