Finite Abelian Group Labeling of Graphs

By : Purnima Gupta, Mukti Acharya, Pranjali

Page No: 167-174

Abstract
In this paper, we have introduced a new type of labeling called an abelian group labeling, in which the operation on vertex labels vary according to the nature of the group. Viewed in this way, the unitary addition Cayley graph turns out to be maximal with respect to an abelian group labeling. Further, we have shown that every finite graph admits an abelian group labeling. Furthermore, we found that representation labeling can be obtained from abelian group labeling for certain graphs. Several new directions for further research are also indicated through problems.

Authors :
Pranjali : Department of Mathematics, University of Delhi, Chhatra Marg, Delhi-110007, India.
Mukti Acharya : Former Professor and Head, Department of Applied Mathematics, Delhi Technological University Delhi-110042, India.
Purnima Gupta : Department of Mathematics, Sri Venkateswara College, University of Delhi-110021, India.