Commutative rings with ideal based zero divisor graph of orders 12,13 and 14

Abstract

An recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs. Although significant progress has been made for rings with degrees up to 11, the exploration of this classification for degrees 12, 13, and 14 is still a subject of on going study. In this work, we study the other type of graph of commutative ring called the ideal based zero divisor graph denoted by Г_I (R ). J. Smith investigated the ideal based zero divisor graph of vertices less than or equal 7. In this work, also we used Г_I (R )orders 12,13 and 14 to find all possible rings with respect to ideal I. To represent Г_I (R ), utilize the characteristic| V(Г_I (R ))|=| I |∙|V(Г( R / I ) |

Keywords

• ideal based zero divisor graph
• zero divisor graph
• non-local ring
• finite direct product
• order of a graph