Advances and Applications in Discrete Mathematics
Volume 30, , Pages 59 - 79
(April 2022) http://dx.doi.org/10.17654/0974165822019 |
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INTERSECTION GRAPH OF γ-SETS IN THE TOTAL GRAPH OF WITH RESPECT TO NIL IDEAL
Arijit Mishra and Kuntala Patra
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Abstract: For any non-reduced ring the total graph of with respect to nil ideal, denoted by is a simple, undirected graph having vertex set and any two distinct vertices x and y of are adjacent if and only if where denotes the nil ideal of In this paper, we introduce a new class of graphs called intersection graphs. The intersection graph of g-sets of denoted by is a simple, undirected graph in which all the g-sets of are taken as vertices and any two distinct vertices and are adjacent if and only if they have non-empty intersection, i.e., We show that the intersection graph is Eulerian for every non-reduced We also characterize the values of n for which the graph is planar. We also obtain the diameter, girth, domination, independence and clique numbers of these graphs.
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Keywords and phrases: total graph, nil ideal, domination number, independence number, intersection graph. |
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