### The intersection graph of a 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.

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.

#### Keywords

Loop theory, Intersection graph, Finite Moufang loop.

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