2018, Vol. 3, Issue 2, Part F
A study of line graph theory towards line set domination
Author(s): Roji Lather
Abstract: We introduce the concept of domatic number in
LG. The minimum cardinality of vertices in such a set is called a split line domination number in
L (G) and is denoted by
γsl (G). In this paper, we introduce the new concept in domination theory. Also, we study the graph theoretic properties of
γ sl (G) and many bounds were obtained in terms of elements of
G and its relationships with other domination parameters were found. For any graph
G, the line graph
L G H is the intersection graph. Thus the vertices of
LG are the edges of
G, with two vertices of LG adjacent whenever the corresponding edges of
G are. A dominating set
D is called independent dominating set of
LG, if
D is also independent. The independent domination number of
LG denoted by i
LG, equals min
{; DD is an independent dominating set of
LG}. Adomatic partition of LG is a partition of VLG, all of whose classes are dominating sets in
LG. The maximum number of classes of a domatic partition of
LG is called the domatic number of
LG and denoted by d
LG. In this paper many bounds on i
LG were obtained in terms of elements of G, but not in terms of elements of
LG. Further we develop its relationship with other different domination parameters.
Pages: 443-445 | Views: 1256 | Downloads: 14Download Full Article: Click Here
How to cite this article:
Roji Lather. A study of line graph theory towards line set domination. Int J Stat Appl Math 2018;3(2):443-445.
