Bounds on several versions of restrained domination number

Authors

  • Babak Samadi Arak University
  • Hamid R Golmohammadi Department of Mathematics University of Tafresh, Tafresh, IRI
  • Abdollah Khodkar Department of Mathematics University of West Georgia Carrollton, GA 30118, USA

DOI:

https://doi.org/10.11575/cdm.v12i1.62175

Keywords:

restrained domination, restrained double domination, total restrained domination

Abstract

We investigate several versions of restrained

domination numbers and present new bounds on these parameters. We generalize the

concept of restrained domination and improve some well-known bounds in the literature.

In particular, for a graph $G$ of order $n$ and minimum degree $\delta\geq 3$, we prove that

the restrained double domination number of $G$ is at most $n-\delta+1$. In addition,

for a connected cubic graph $G$ of order $n$ we show that

the total restrained domination number of $G$ is at least $n/3$ and

the restrained double domination number of $G$ is at least $n/2$.

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Published

2017-09-27

Issue

Vol. 12 No. 1 (2017)

Section

Articles

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