Coprime graph of subgroups of a group

R. Rajkumar; P. Devi

Coprime graph of subgroups of a group

Group Theory 2015-12-08 v2

Authors: R. Rajkumar , P. Devi

Abstract

Let $G$ be a group. We define the coprime graph of subgroups of $G$ , denoted by $\mathcal P(G)$ , is a graph whose vertex set is the set of all proper subgroups of $G$ , and two distinct vertices are adjacent if and only if the order of the corresponding subgroups are coprime. In this paper, we study some connections between algebraic properties of a group and graph theoretic properties of its coprime graph.

Keywords

coprime graph subgroup group theory graph theory algebraic property vertex set adjacency relation

Cite

@article{arxiv.1510.00129,
  title  = {Coprime graph of subgroups of a group},
  author = {R. Rajkumar and P. Devi},
  journal= {arXiv preprint arXiv:1510.00129},
  year   = {2015}
}

Comments

18 pages, 7 figures, title changed, a new section added

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