IJPAM: Volume 98, No. 4 (2015)

ON GRAPHS WITH BINDING NUMBER ONE

H.B. Walikar$^1$, B.B. Mulla$^2$
$^1$Department of Mathematics
Karnatak University
Dharwad, 580003
Karnataka State, INDIA
$^2$Department of Mathematics
Smt. Indira Gandhi College of Engineering
Sector-16, Koparkhairane, Navi Mumbai-400709
Maharashtra State, INDIA


Abstract. I. Anderson (see [#!Ander!#]) asked to study class of graphs with binding number one. We characterize bipartite graphs with binding number one and prove that graphs with binding number one cannot be characterized in terms of forbidden subgraphs by embedding an arbitrary graph $G$ in a graph $H$ with binding number one. We obtain bounds on the size of a graph with binding number one. I. Anderson [#!Ander!#] has defined any graph $G$ to be binding minimal if

\begin{displaymath}bind\left(G-x\right)<bind\left(G\right).\end{displaymath}



Received: March 24, 2014

AMS Subject Classification: 05C

Key Words and Phrases: graph, binding number

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DOI: 10.12732/ijpam.v98i4.1 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: 98
Issue: 4
Pages: 413 - 418


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