Title: Very cost effective bipartition in Gamma(Z_n),
Abstract: Let Z_n be the finite commutative ring of residue classes modulo n and
Gamma(Z_n) be its zero-divisor graph. The nilradical graph and non-nilradical
graph of Z_n are denoted by N(Z_n) and Omega(Z_n) respectively. In 2012, Haynes
et al. [5] introduced the concept of very cost effective graph. For a graph G =
(V,E) and a set of vertices S subset of V, a vertex v in S is said to be very
cost effective if it is adjacent to more vertices in V§than in S. A
bipartition Pi = {S, V§} is called very cost effective if both S and V§are
very cost effective sets [5,6]. In this paper, we investigate the very cost
effective bipartition of Gamma(Z_n), where n = p_1 p_2 ... p_m, here all p_i's
are distinct primes. In addition, we discuss the cases in which N(Z_n) and
Omega(Z_n) graphs have very cost effective bipartition for different n.
Finally, we derive some results for very cost effective bipartition of the Line
graph and Total graph of Gamma(Z_n), denoted by L(Gamma(Z_n)) and T(Gamma(Z_n))
respectively.