@Article{iasc.2021.019391,
AUTHOR = {Azeem Haider, Ali N.A. Koam, Ali Ahmad},
TITLE = {Radio Labeling Associated with a Class of Commutative Rings Using Zero-Divisor Graph},
JOURNAL = {Intelligent Automation \& Soft Computing},
VOLUME = {30},
YEAR = {2021},
NUMBER = {3},
PAGES = {787--794},
URL = {http://www.techscience.com/iasc/v30n3/44106},
ISSN = {2326-005X},
ABSTRACT = {Graph labeling is useful in networks because each transmitter has a different transmission capacity to send or receive wired or wireless links. An interference of signals can occur when transmitters that are close together receive close frequencies. This problem has been modeled mathematically in the radio labeling problem on graphs, where vertices represent transmitters and edges indicate closeness of the transmitters. For this purpose, each vertex is labeled with a unique positive integer, and to minimize the interference, the difference between maximum and minimum used labels has to be minimized. A radio labeling for a graph  is a function  from the set of vertices  to the set of positive integers satisfying the condition , where  is the shortest distance between two distinct vertices , and  is the diameter of the graph  The minimum span of a radio labeling for  is called the radio number of  Because the problem of finding radio labeling appears to be difficult in general, many particular cases have been studied. Let  be a commutative ring with nonzero identity, and  its set of (nonzero) zero-divisors. The zero-divisor graph of a ring  is the graph  with vertex set  and edge set . In this paper, we investigate the radio number for an associated zero-divisor graph, . The study provides some combinatorial properties associated with commutative rings and can be useful for the structures of network communication problems.},
DOI = {10.32604/iasc.2021.019391}
}