Korean J. Math. Vol. 30 No. 1 (2022) pp.53-60
DOI: https://doi.org/10.11568/kjm.2022.30.1.53

Line graphs of unit graphs associated with the direct product of rings

Main Article Content

Shariefuddin Pirzada
Aaqib Altaf


Let $R$ be a finite commutative ring with non zero identity. The unit graph of $R$ denoted by $G(R)$ is the graph obtained by setting all the elements of $R$ to be the vertices of a graph and two distinct vertices $x$ and $y$ are adjacent if and only if $x+y \in U(R)$, where $U(R)$ denotes the set of units of $R$. In this paper, we find the commutative rings $R$ for which $G(R)$ is a line graph. Also, we find the rings for which the complements of unit graphs are line graphs.

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