ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 9 (2020), no.8, 5901–5908 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.9.8.57 Special Issue on ICMA-2020 THE CYLINDRICAL CROSSING NUMBER OF ZERO DIVISOR GRAPHS MARIA SAGAYA NATHAN 1 AND J. RAVI SANKAR 2 ABSTRACT. The concept of zero divisor was started in 1988 by Beck. He intro- duced this idea to coloring a commutative ring by using simple graphs and also included zero to the set vertices of zero divisors.Few years later, that is in 1999 Anderson and Livingston applied slight modification to Beck’s definition by re- stricting the vertices set only to the nonzero zero divisors of the ring. In this paper we discuss about the cylinderical crossing number of zero divisor graphs for some graphs. 1. BASIC DEFINITIONS Definition 1.1. A simple graph in which each pair of distinct vertices is joined by an edge is called a complete graph. A complete graph on n vertices is denoted by K n . Definition 1.2. A graph G is called bipartite if its vertex set V can be decomposed into two disjoint subsets V 1 , V 2 such that every edge in G joins a vertex in V 1 with a vertex in V 2 .A complete bipartite graph is a bipartite graph with bipartition (V 1 ,V 2 ) such that every vertex of V 1 is joined to all the vertices of V 2 . It is denoted by K m,n , where |V 1 | = m and |V 1 | = n. A star graph is a complete bipartite K 1,n . Definition 1.3. A graph G is a k-partite graph is V(G) can be partitioned into k subsets V 1 ,V 2 , ....,V k such that uv is an edge of G if u and v belong to different 2 Corresponding author 2010 Mathematics Subject Classification. 05C10. Key words and phrases. Zero divisor, Crossing Number. 5901