$K_4$-free character graphs with seven vertices
Mahdi Ebrahimi

TL;DR
This paper classifies all finite groups with seven-vertex character graphs that do not contain a complete subgraph of four vertices, providing a comprehensive understanding of their structure and possible graph configurations.
Contribution
It determines the structure of all finite groups with $K_4$-free seven-vertex character graphs and classifies all such graphs realizable as character graphs.
Findings
Complete classification of groups with $K_4$-free seven-vertex character graphs
Identification of all possible $K_4$-free graphs as character graphs
Structural descriptions of these groups and graphs
Abstract
For a finite group , let denote the character graph built on the set of degrees of the irreducible complex characters of . In this paper, we determine the structure of all finite groups with -free character graph having seven vertices. We also obtain a classification of all -free graphs with seven vertices which can occur as character graphs of some finite groups.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Coding theory and cryptography
