The Total Merging Number of Zero Divisor Graphs

Abstract

The notion of zero divisors was initiated by Beck in 1988. He introduced 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 their idea to change Beck's definition by restricting the vertices set only to the nonzero zero divisors of the ring. In his paper we discuss about the total merging number of complete and complete bipartite graphs with the zero divisor graphs.