The mdeficient number of complete bigraphs

Full Text(PDF, 3000) PP.


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 mdeficient number interpolates or not. A negative answer of this problem is established in [5]. The counter example in [5] was obtained by characterizing the mdeficient number of complete graph. In this note another counter example was obtained by characterizing the mdeficient number of complete bipartite graphs Kn1, n2, n1? n2 in a similar way.


References 

[1] D.G Akka and Nanda S. Warad, The mdeficient number of
graphs, Graph Theory Notes of New York, LVI (2009)1516,
[2] M. Aaron and M. Lewinter, odeficient vertices of spanning
trees, Graph Theory Notes of New York, xxvii : 5, New York
Academy of Sciences (1994) 3132
[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, Cas34 (1987)205.
[5] J.Yuan, A note on a problem of Aaron and Lewinter about
the mdeficient number of graphs, Graph Theory Notes of
New York, xxviii : 9, New York


