Geodesic
On the Non-Inverse Graph of a Group
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 315-325

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Let (G, *) be a finite group and S = u ∈ G|u ≠ u−1, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. In this paper, we introduce a modified version of the inverse graph, called i*-graph associated with a group G. The i*-graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ∈ Γ are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i*-graph are also determined.
Keywords: inverse graph, non-inverse graph 
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Amreen, Javeria; Naduvath, Sudev. On the Non-Inverse Graph of a Group. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 315-325. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a4/