\(k\)-Odd Edge Mean Labeling of Some Basic Graphs
DOI:
https://doi.org/10.26713/jims.v9i3.1012Keywords:
\(k\)-Odd edge mean labeling, \(k\)-Odd edge mean graphAbstract
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.Downloads
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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