## Connected domination in litact graph

#### AUTHOR AND AFFILIATION

M.H. MUDDEBIHAL and NAILA ANJUM
Department of Mathematics Gulbarga University Gulbarga Karnataka India

Email:-mhmuddebihal@yahoo.co.in

#### KEYWORDS:

Litact graph, domination number, connected domination number. Subject classification number:AMS -05C69,05C70

December 2012

#### ISSN:

2319-8044 (Online) – 2231-346X (Print)

Vol.24 – No.3

jusps-A

#### ABSTRACT:

Let be a connected graph. The litact graph m(G) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut vertices of G in which two vertices are adjacent if and only if the corresponding members of G are adjacent or incident. A dominating set D of m (G) is called a connected dominating set of m (G) if the induced subgraph is connected. The minimum cardinality of D is called the connected domination number of m (G) and is denoted by . In this paper, we initiate a study of this parameter. We obtain many bonds on in terms of vertices, edges and different parameters of G and not the members of m (G). Further we determine its relationship with other domination parameters.

#### Copy the following to cite this Article:

M.H. MUDDEBIHAL and NAILA ANJUM, “Connected domination in litact graph”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 3, Page Number , 2016

#### Copy the following to cite this URL:

M.H. MUDDEBIHAL and NAILA ANJUM, “Connected domination in litact graph”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 3, Page Number , 2016

Available from: http://www.ultrascientist.org/paper/553/

Let be a connected graph. The litact graph m(G) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut vertices of G in which two vertices are adjacent if and only if the corresponding members of G are adjacent or incident. A dominating set D of m (G) is called a connected dominating set of m (G) if the induced subgraph is connected. The minimum cardinality of D is called the connected domination number of m (G) and is denoted by . In this paper, we initiate a study of this parameter. We obtain many bonds on in terms of vertices, edges and different parameters of G and not the members of m (G). Further we determine its relationship with other domination parameters.