Cordial Labeling of One Point Union of Some Graphs

G. V. Ghodasara; A. H. Rokad

doi:https://doi.org/10.14445/22315373/IJMTT-V11P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 11 | Number 1 | Year 2014 | Article Id. IJMTT-V11P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P509

Cordial Labeling of One Point Union of Some Graphs

G. V. Ghodasara, A. H. Rokad

Abstract

A graph G in which a vertex is distinguished from other vertices is called a rooted graph and the vertex is called the root of G. Let G be a rooted graph. The graph G(n) obtained by identifying the roots of n copies of G is called the one-point union of n copies of the graph G. A function from vertex set of a graph to the set {0, 1}, which assigns the label |f(u) − f(v)| for each edge uv, is called a cordial labeling of the graph if the number of vertices labeled 0 and number of vertices labeled 1 differ by at most 1, and similar condition is satisfied by the edges of the graph. In this paper we discuss cordial labeling of one point union of grid graph, cycle with one chord and cycle with twin chords.

Keywords

Cordial graph, One Point Union AMS Subject classification number: 05C78.

References

[1] I. Cahit, ”Cordial Graphs: A weaker version of graceful and Harmonic Graphs”, Ars Combinatoria, 23(1987) 201-207.
[2] I. Cahit, ”On cordial and 3-equitable labellings of graphs”, Util. Math., 37(1990) 189-198.
[3] J. A. Gallian, ”A dynemic survey of graph labeling”, The Electronics Journal of Combinatorics, 16(2013), ]DS6 1 − 308.
[4] G. V. Ghodasara, A. H. Rokad and I. I. Jadav, ”Cordial labeling of grid related graphs”, International Journal of Combinatorial Graph Theory and Applications, 6(2013) 55-62.
[5] Jonathan L. Gross and Jay Yellen, ”Graph Theory and Its Applications, Second Edition”, CRC Press, 1998.
[6] S. C. Shee and Y. S. Ho, The cordiality of onepoint union of n-copies of a graph, Discrete Math., 117 (1993) 225-243.
[7] P. Selvaraju, New classes of graphs with - valuation, harmonious and cordial labelings, Ph. D. Thesis, Anna University, 2001. Madurai Kamaraj University, 2002.
[8] M. Benson and S. M. Lee, On cordialness of regular windmill graphs, Congress. Numer., 68 (1989) 45-58.

Citation :

G. V. Ghodasara, A. H. Rokad, "Cordial Labeling of One Point Union of Some Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 1, pp. 67-70, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P509