IJPAM: Volume 101, No. 4 (2015)



Karnatak University
Dharwad, 580003, Karnataka State, INDIA

Smt. Indira Gandhi College of Engineering
Sector-16, Koparkhairane, Navi Mumbai, 400709, Maharashtra State, INDIA
Abstract. V.G. Kane (see [#!Kane!#]) asked to study the class of graphs satisfying
. Here we determine binding number of power of various classes of graphs along with the solution for the parametric equation
. We also show that
if and only if
, where
is the graph obtained from
by adjoining a pendant edge to each vertex of
, by proving that the diophantine equation
has no nontrivial integral solution. In Theorem 3.4, we prove that there exists no graph
such that
for
by seeking integral solution for
.
Received: November 11, 2014
AMS Subject Classification: 05C
Key Words and Phrases: binding number, power, hallian index
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DOI: 10.12732/ijpam.v101i4.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 4
Pages: 505 - 511
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This work is licensed under the Creative Commons Attribution International License (CC BY).