Cyclic Subgroup Graph of a Group

Khyati Sharma; A. Satyanarayana Reddy

Cyclic Subgroup Graph of a Group

Group Theory 2024-09-24 v1 Combinatorics

Authors: Khyati Sharma , A. Satyanarayana Reddy

Abstract

A cyclic subgroup graph of a group $G$ is a graph whose vertices are cyclic subgroups of $G$ and two distinct vertices $H_1$ and $H_2$ are adjacent if $H_1\leq H_2$ , and there is no subgroup $K$ such that $H_1<K<H_2$ . M.T\u{a}rn\u{a}uceanu gave the formula to count the number of edges of these graphs. In this paper, we explore various properties of these graphs.

Keywords

graph theory of groups graph cycles hamilton cycles

Cite

@article{arxiv.2409.13796,
  title  = {Cyclic Subgroup Graph of a Group},
  author = {Khyati Sharma and A. Satyanarayana Reddy},
  journal= {arXiv preprint arXiv:2409.13796},
  year   = {2024}
}

Comments

14 Pages

Cyclic Subgroup Graph of a Group

Abstract

Keywords

Cite

Comments

Related papers