Linear representation of groups associated to graphs

Alain Bretto; Alain Faisant; Neda Moradi; Mehrdad Nasernejad

Linear representation of groups associated to graphs

Representation Theory 2026-06-18 v1 Combinatorics

Authors: Alain Bretto , Alain Faisant , Neda Moradi , Mehrdad Nasernejad

Abstract

In this article, we introduce a group linear representation associated to a graph. We study this representation as well as the canonical decomposition of the associated module. A character study is conducted, demonstrating the relevance of this approach to graph theory. We also develop the links that exist between algebra and graphs, particularly in the language of representations.

Cite

@article{arxiv.2607.15287,
  title  = {Linear representation of groups associated to graphs},
  author = {Alain Bretto and Alain Faisant and Neda Moradi and Mehrdad Nasernejad},
  journal= {arXiv preprint arXiv:2607.15287},
  year   = {2026}
}