Random Articles
Reseach Article
Balanced Labeling and Balance Index Set of One Point Union of Two Complete Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 52 - Number 13 |
| Year of Publication: 2012 |
| Authors: Pradeep G. Bhat, Devadas Nayak C |
10.5120/8266-1815
|
Pradeep G. Bhat, Devadas Nayak C . Balanced Labeling and Balance Index Set of One Point Union of Two Complete Graphs. International Journal of Computer Applications. 52, 13 ( August 2012), 1-5. DOI=10.5120/8266-1815
Abstract
Let G be a graph with vertex set V (G) and edge set E(G), and consider the set A = f0; 1g. A labeling f : V (G) ! A induces a partial edge labeling f : E(G) ! A defined by f (xy) = f(x), if and only if f(x) = f(y), for each edge xy 2 E(G). For i 2 A, let vf (i) = jfv 2 V (G) : f(v) = igj and ef (i) = je 2 E(G) : f (e) = ij. A labeling f of a graph G is said to be friendly if jvf (0) . . vf (1)j 1. A friendly labeling is called balanced if jef (0) . . ef (1)j 1. The balance index set of the graph G, Bl(G), is defined as fjef (0). . ef (1)j: the vertex labeling f is friendlyg. We provide balanced labeling and balance index set of one point union of two complete graphs.
References
- L. W. Beineke and S. M. Hegde. Strongly multiplicative graphs. Discuss. Math. Graph Theory, 21:63–75, 2001.
- I. Cahit. Cordial graphs: a weaker version of graceful and harmonious graphs. Ars Combin. , 23:201–207, 1987.
- J. A. Gallian. A dynamic survey of graph labeling. The Electronics Journal of Combinatorics, 16(DS6), 2009.
- Frank Harary. Graph Theory. Narosa Publishing House, 1989.
- R. Y. Kim, S-M. Lee, and H. K. Ng. On balancedness of some family of graphs. Manuscript.
- Alexander Nien-Tsu Lee, Sin-Min Lee, and Ho Kuen Ng. On the balance index set of graphs. J. Combin. Math. Combin. Comp. , 66:135–150, 2008.
- S-M. Lee, A. Liu, and S. K. Tan. On balanced graphs. J. Combin. Math. Combin. Comp. , 87:59–64, 2008.
Index Terms
Keywords