Journals Information
Mathematics and Statistics Vol. 13(5), pp. 420 - 424
DOI: 10.13189/ms.2025.130518
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Independent Domination Number of Certain Graphs and Their Degree Splitting Graphs
M. Sridevi 1, N. Srinivasan 2, Parthiban A 3,*
1 Research Scholar, Department of Mathematics, St. Peter's Institute of Higher Education and Research, Avadi, Chennai-600 054, Tamil Nadu, India
2 Department of Mathematics, St. Peter's Institute of Higher Education and Research, Avadi, Chennai-600 054, Tamil Nadu, India
3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India
ABSTRACT
The concept of domination in graphs is an inevitable topic in the field of graph theory. The sources of domination can be seen in a wide range of real-world situations, such as radio broadcasting, computer communication networks, school bus routing, electrical power networks, influence in social networks, surveying, resource allocation, and even transporting hazardous materials. A dominating set (DS) of a finite, simple, connected, and undirected graph 
, or simply 
with a non-empty node set 
and line set 
, is a set 
such that every node, 
is adjacent to a node, 
. The domination number (DN) of , represented by 
, is the cardinality of a minimum DS. Similarly, set 
of nodes is called an independent set (IS) if no two nodes in 
are adjacent to each other. An independent dominating set (IDS) of is a set 
that is both dominating and independent in . The independent domination number (IDN) of , represented by 
, is the cardinality of a minimum IDS. Further, let be with node set 
where each 
is a set of nodes having at least two nodes of the same degree and 
. The degree splitting graph (DSG) of , denoted by 
, is formed from by adding nodes 
and joining to each node of for 
. In this paper, we derive the IDN of certain graphs such as lotus graph, line graph of sunlet graph, butterfly graph, shipping graph, ladder graph, fan graph, double fan graph, and their degree splitting graphs.
KEYWORDS
Graph, Domination in Graphs, Independent Domination, Independent Domination Number, Degree Splitting Graph of a Graph
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] M. Sridevi , N. Srinivasan , Parthiban A , "Independent Domination Number of Certain Graphs and Their Degree Splitting Graphs," Mathematics and Statistics, Vol. 13, No. 5, pp. 420 - 424, 2025. DOI: 10.13189/ms.2025.130518.
(b). APA Format:
M. Sridevi , N. Srinivasan , Parthiban A (2025). Independent Domination Number of Certain Graphs and Their Degree Splitting Graphs. Mathematics and Statistics, 13(5), 420 - 424. DOI: 10.13189/ms.2025.130518.