UNI-LABELING OF GRAPHS OVER FINITE COMMUTATIVE RINGS
UNI-LABELING OF GRAPHS
Abstract
This paper introduces the notion of uni-labeling of a graph and its empirical study demonstrates that every finite graph admits a uni-labeling with respect to some finite commutative ring. In the course of the investigation, it is found that unit graph turns out to be maximal with respect to the optimal uni-labeling index. Furthermore, the paper determines the optimal uni-labeling index for several well-known families of graphs. Several new directions for further research are also indicated through problems.
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