Isolate restrained domination in graphs
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https://doi.org/10.26637/MJM0901/0211Abstract
A dominating set \(D\) of a graph \(G\) is said to be a restrained dominating set (RDS) of \(G\) if every vertex of \(V-D\) has a neighbor in \(V-D\). A RDS is said to be an isolate restrained dominating set(IRDS) if \(<D>\) has at least one isolated vertex.
The minimum cardinality of a minimal IRDS of \(G\) is called the isolate restrained domination number(IRDN), denoted by \(\gamma_{r,0}(G)\). This paper contains basic properties of IRDS and gives the IRDN for the families of graphs such as paths, cycles, complete \(k\)-partite graphs and some other graphs.
Keywords:
Restrained domination, isolate domination, isolate domination numberMathematics Subject Classification:
Mathematics- Pages: 1221-1224
- Date Published: 25-03-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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