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International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 10    
Website: http://www.ijser.org
scirp IJSER >> Volume 2, Issue 10, October 2011 Edition
The m-deficient number of complete bigraphs
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Author(s)
Sanjay Roy, Dr. Danappa G.Akka
KEYWORDS
Interpolate, deficient number, Degree preserving
ABSTRACT
An open problem posed by Aaron and Lewinter in [2] asks whether the m-deficient number interpolates or not. A negative answer of this problem is established in [5]. The counter example in [5] was obtained by characterizing the m-deficient number of complete graph. In this note another counter example was obtained by characterizing the m-deficient number of complete bipartite graphs Kn1, n2, n1? n2 in a similar way.
References
[1] D.G Akka and Nanda S. Warad, The m-deficient number of graphs, Graph Theory Notes of New York, LVI (2009)15-16,

[2] M. Aaron and M. Lewinter, o-deficient vertices of spanning trees, Graph Theory Notes of New York, xxvii : 5, New York Academy of Sciences (1994) 31-32

[3] J.A Bondy and U.S.R. Murthy, Graph Theory with Applications, Macmillan, London (1976).

[4] M. Lewinter, Interpolation theorem for the number of degree- preserving vertices of spanning tree, IEEE Tran. Circuits system, Cas-34 (1987)205.

[5] J.Yuan, A note on a problem of Aaron and Lewinter about the m-deficient number of graphs, Graph Theory Notes of New York, xxviii : 9, New York

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