Advances and Applications in Discrete Mathematics
Volume 24, Issue 2, Pages 99 - 115
(July 2020) http://dx.doi.org/10.17654/DM024020099 |
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THE DOUBLE TOTAL GRAPH OF A COMMUTATIVE RING
Ngangom Rojitkumar Singh and Sanghita Dutta
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Abstract: In this paper, we introduce the double total graph of a finite commutative ring R with non-zero unity, denoted by which is an undirected graph with vertex set R and any two distinct elements x and y in R are adjacent if and only if for some We investigate connectedness, diameter, girth and domination parameter of We show that is complete if and only if R is a reduced unit fusible ring with In particular, we investigate the basic properties of Also, we characterize R in terms of planarity of |
Keywords and phrases: fusible ring, unit graph, total graph, double total graph.
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