# $k$-odd mean labeling of prism

Document Type: Research Paper

Authors

1 Periyar E.V.R. College(Autonomous)

2 Roever Engineering College

Abstract

‎A $(p,q)$ graph $G$ is said to have a $k$-odd mean‎ ‎labeling $(k \ge 1)$ if there exists an injection $f‎ : ‎V‎ ‎\to \{0‎, ‎1‎, ‎2‎, ‎\ldots‎, ‎2k‎ + ‎2q‎ - ‎3\}$ such that the‎ ‎induced map $f^*$ defined on $E$ by $f^*(uv) =‎ ‎\left\lceil \frac{f(u)+f(v)}{2}\right\rceil$ is a‎ ‎bijection from $E$ to $\{2k‎ - ‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎\ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3\}$‎. ‎A  graph that admits $k$-odd mean‎ ‎labeling is called $k$-odd mean graph‎. ‎In this paper‎, ‎we investigate $k$-odd mean labeling of prism $C_m \times P_n$‎.

Keywords

Main Subjects

### References

[1] K. Amuthavalli, Graph labeling and its applications-Some generalization of odd mean labeling, Ph. D. Thesis, Mother Teresa Womens University, 2010.

[2] G. S. Bloom and S. W. Golomb, Numbered complete graphs, unusual rulers and assorted applications, Theory and Applications of Graphs, Lecture notes in Mathematics,642, Springer, Berlin, 1978 53–65.

[3] G. S. Bloom and S. W. Colomb, Applications of Numbered undirected graphs, Proceedings of IEEE, 65 (1977) 562–570.

[4] G. S. Bloom and D. F. Hsu, On graceful digraphs and a problem in network addressing, Congr. Numer., 35 (1982) 91–103.

[5] A. J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin., Dynamic Survey, 5 (1998) pp. 43.

[6] B. Gayathri and K. Amuthavalli, $k$-odd mean labeling of graphs, Proceedings of the International Conference on Mathematics and Computer Science-2, Sitech Publications, 2007 112–115.

[7] B. Gayathri and K. Amuthavalli, $(k,d)$-odd mean labeling of graphs, National Symposium on Mathematical Methods and Applications, I.I.T., Chennai, 2006.

[8] B. Gayathri and K. Amuthavalli, $k$-odd mean labeling of Crown graphs, Int. J. Math. Comput. Sci., 2 no. 3 (2007) 253–259.

[9] B. Gayathri and K. Amuthavalli, $(k,d)$-odd mean labeling of some graphs, Bull. Pure Appl. Sci. Sect. E Math. Stat., 26 no. 2 (2007) 263–267.

[10] B. Gayathri and K. Amuthavalli, $k$-odd mean labeling of $⟨K_{1,n},K_{1,m}⟩$, Acta Cienc. Indica Math., 34 no. 2 (2008) 827–834.

[12] K. Manickam and M. Marudai, Odd mean labelings of graphs, Bull. Pure Appl. Sci. Sect. E Math. Stat., 25 no. 1 (2006) 149–153.

[13] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs Internat. Sympos., Rome, 1966), Gordon and Breach, New York; Dunod, Paris, 1967 349–355.

[14] S. Somasundaram and R. Ponraj, Mean Labeling of graphs, Nat. Acad. Sci. Lett., 26 no. 7-8 (2003) 210–213.