Abstract
This paper introduces the notions of a zero-divisor labeling and the zero-divisor index of a graph using the zero-divisors of a commutative ring. Viewed in this way, the usual zero-divisor graph is a maximal graph with respect to a zero-divisor labeling. We also study optimal zero-divisor labelings of a finite graph.
ACKNOWLEDGMENTS
Gratitude is extended to Dr. Mukti Acharya (Former Head and Professor Delhi Technological University, Delhi, India) for giving helpful suggestions. The first author is also thankful to the Department of Atomic Energy (DAE) for providing the research grant with sanctioned letter number: 2/39(26)/2012 -R&D-II/4114.