The intersection graph of a finite Moufang loop

Authors

  • Hamideh Hasanzadeh Islamic Azad University,
  • Ali Iranmanesh Tarbiat Modares University

DOI:

https://doi.org/10.30495/jme.v14i0.1130

Keywords:

Loop theory, Intersection graph, Finite Moufang loop.

Abstract

The intersection graph ΓSI(G) of a group G with identity element e is the
graph whose vertex set is the set V (ΓSI(G)) = G-e and two distinct vertices x
and y are adjacent in ΓSI(G) if and only if |⟨x⟩∩⟨y⟩| > 1; where ⟨x⟩ is the cyclic
subgroup of G generated by x. In this paper, at first we obtain some results
for this graph for any Moufang loop. More specially we observe non-isomorphic
finite Moufang loops may have isomorphic intersection graphs.

Author Biographies

Hamideh Hasanzadeh, Islamic Azad University,

Department of Mathematics, Science and Research Branch, Islamic Azad University,

Ali Iranmanesh, Tarbiat Modares University

Department of Mathematics, Tarbiat Modares University, Tehran, Iran .
Professor

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Published

2019-04-10

Issue

Vol. 14

Section

Vol. 14, No. 2, (2020)

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