Call for Paper - March 2023 Edition
IJCA solicits original research papers for the March 2023 Edition. Last date of manuscript submission is February 20, 2023. Read More

# Balanced Labeling and Balance Index Set of One Point Union of Two Complete Graphs

International Journal of Computer Applications
Volume 52 - Number 13
Year of Publication: 2012
Authors:

Pradeep G Bhat and Devadas Nayak C. Article: Balanced Labeling and Balance Index Set of One Point Union of Two Complete Graphs. International Journal of Computer Applications 52(13):1-5, August 2012. Full text available. BibTeX

```@article{key:article,
title = {Article: Balanced Labeling and Balance Index Set of One Point Union of Two Complete Graphs},
journal = {International Journal of Computer Applications},
year = {2012},
volume = {52},
number = {13},
pages = {1-5},
month = {August},
note = {Full text available}
}
```

### 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.

### Keywords

Learn about the IJCA article correction policy and process
Dealing with any form of infringement.
‘Peer Review – A Critical Inquiry’ by David Shatz
Directly place requests for print/ hard copies of IJCA via Google Docs