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http://dx.doi.org/10.11568/kjm.2022.30.1.53

LINE GRAPHS OF UNIT GRAPHS ASSOCIATED WITH THE DIRECT PRODUCT OF RINGS  

Pirzada, S. (Department of Mathematics, University of Kashmir)
Altaf, Aaqib (Department of Mathematics, University of Kashmir)
Publication Information
Korean Journal of Mathematics / v.30, no.1, 2022 , pp. 53-60 More about this Journal
Abstract
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 ∈ 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.
Keywords
Ring of integers modulo; zero-divisor graph; unit graph; line graph;
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Times Cited By KSCI : 3  (Citation Analysis)
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