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 (p,q) graph G is said to have a k-odd edge mean labeling (k≥1), if there exists an injection f from the edges of G to {0,1,2,3,…,2k+2p−3} such that the induced map f∗ defined on V by f∗(v)=⌈∑f(vu)deg⁡(v)⌉ is a bijection from V to {2k−1,2k+1,2k+3,…,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.

J.A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics 18 (2014), # DS6.

B. Gayathri and K. Amuthavalli, (k,d)-odd mean labeling of some graphs, Bulletin of Pure and Applied Sciences 26E (2) (2007), 263 – 267.

B. Gayathri and K. Amuthavalli, k-odd mean labeling of crown graphs, International Journal of Mathematics and Computer Science 2 (3) (2007), 253 – 259.

F. Harary, Graph Theory, Addison-Wesley, Reading Masaachusetts (1972).

K. Manickam and M. Marudai, Odd mean labeling of graphs, Bulletin of Pure and Applied Sciences 25E (1) (2006), 149 – 153.

A. Rosa, On certain valuations of the vertices of a graph, in Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N.Y. and Dunod Paris (1967), pp. 349 – 355.

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

Vol. 9 No. 3 (2017)

Section

Research Article

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