# IJPAM: Volume 41, No. 4 (2007)

**THE DOMINATION NUMBER OF CONNECTED GRAPHS**

Department of Mathematics

Mahidol Wittayanusorn School

Salaya, Nakhon Pathom, 73170, THAILAND

Department of Mathematics and Statistics

Faculty of Science and Technology

Thammasat University

Rangsit, Pathumthani, 12120, THAILAND

e-mail: araya@mathstat.sci.tu.ac.th

**Abstract.**Let be the domination number of a graph and
be the class of all non-isomorphic connected graphs of
order and size .
Punnim [#!NP!#] proved that for any positive integers
and with
,
there exist positive integers and in which there
exists a graph such that
if and only if is an integer and
. Thus for any positive integers
and ,
is
uniquely determined by

We are able to find the values of
and
in all situations.

**Received: **September 28, 2007

**AMS Subject Classification: **05C35, 05C69

**Key Words and Phrases: **domination number, interpolation theorem, extremal problem

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2007

**Volume:** 41

**Issue:** 4