The radius, diameter and chromatic number of some zero divisor graph

Document Type : Research Paper


Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq


In this work, the radius, diameter and a chromatic number of zero divisor graph of the ring $Z_n$  for some n are been determined. These graphs are ${\Gamma }\left(Z_{p^2q^2}\right)$,  ${\Gamma }\left(Z_{p^2}\right)$, ${\Gamma}\left(Z_{pq}\right)$, ${\Gamma }\left(Z_{p^3}\right)$, ${\Gamma }\left(Z_{p^2q}\right)$ and ${\Gamma }\left(Z_{pqr}\right)$. Furthermore, the largest induced subgraph isomorphic to complete subgraph in the graph ${\Gamma }\left(Z_{p^3}\right)$  and $\mathit{\Gamma}(p^2q)$ are calculated.