Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Prime Cordial Labeling of Graphs

  • Aljouiee, Abdullah (Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University)
  • Received : 2013.09.27
  • Accepted : 2014.01.29
  • Published : 2016.03.23
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Abstract

A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, $2{\cdots}$, n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm ${\bar{H}}_n$, and present a new way of prime cordial labeling of $P^2_n$. Finally we make a correction of the proof of Theorem 2.5 in [12].

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References

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