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

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International Journal of Computer Applications
© 2012 by IJCA Journal
Volume 52 - Number 13
Year of Publication: 2012
Authors:
Pradeep G. Bhat
Devadas Nayak C
10.5120/8266-1815

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,
	author = {Pradeep G. Bhat and Devadas Nayak C},
	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.

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