\(k\)-Odd Edge Mean Labeling of Some Basic Graphs

Authors

  • K. Amuthavalli PG & Research Department of Mathematics, Government Arts College, Ariyalur, Tamilnadu
  • S. Dineshkumar PG & Research Department of Mathematics, Government Arts College, Ariyalur, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v9i3.1012

Keywords:

\(k\)-Odd edge mean labeling, \(k\)-Odd edge mean graph

Abstract

A \(\left(p,q\right)\) graph \(G\) is said to have a \(k\)-odd edge mean labeling \((k\ge 1)\), if there exists an injection \(f\) from the edges of \(G\) to \(\{0,1,2,3,\ldots,2k+2p-3\}\) such that the induced map \(f^*\) defined on \(V\) by \(f^{*} (v)=\left\lceil \frac{\sum f(vu) }{\deg (v)} \right\rceil\) is a bijection from \(V\) to \(\{2k-1,2k+1,2k+3,\ldots, 2k+2p-3\}\). A graph that admits a \(k\)-odd edge mean labeling is called a \(k\)-odd edge mean graph. In this paper, we have introduced \(k\)-odd edge mean labeling and we have investigated the same labeling for basic graphs like path and star.  Also we have examined the existence and non existence of cycles.

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References

K. Amuthavalli, Graph labeling and its applications - some generalizations of odd mean labelings, Ph.D thesis, Mother Theresa Women's University, Kodaikanal, July 2010.

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S. Somasundaram and R. Ponraj, Mean labeling of graphs, National Academy Science Letter 26 (7-8) (2003), 10 – 13.

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Published

2017-10-30
CITATION

How to Cite

Amuthavalli, K., & Dineshkumar, S. (2017). \(k\)-Odd Edge Mean Labeling of Some Basic Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 915–921. https://doi.org/10.26713/jims.v9i3.1012

Issue

Section

Research Articles