Total Graph of Z_n and It's Adjacency Matrix

Pinku Sarkar, Kuntala Patra

Abstract: Let G be a simple undirected graph. For a commutative ring R, Z(R)be the set of zero divisors of R. Total graph of R is denoted by T(?(R)), all elements of R are taken as vertices of the graph.Two distinct vertices a,b are adjacent if and only if a+b?Z(R). Here we study total graph T(?(R)) for R=Z_n. Also discuss degree, planarity, Eulerian property for different n. We also study adjacency matrix of the graph.

Keywords: Total Graph, Planarity, Adjacency matrix

How to Cite?: Pinku Sarkar, Kuntala Patra, "Total Graph of Z_n and It's Adjacency Matrix", Volume 11 Issue 4, April 2022, International Journal of Science and Research (IJSR), Pages: 1017-1019, https://www.ijsr.net/getabstract.php?paperid=SR22421133351, DOI: https://dx.doi.org/10.21275/SR22421133351