## Abstract

A set S of vertices in a graph G is a dominating set if every vertex not in S is adjacent to a vertex in S. If, in addition, S is an independent set, then S is an independent dominating set. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set in G. In Goddard and Henning (Discrete Math 313:839–854, 2013) conjectured that if G is a connected cubic graph of order n, then i(G)≤38n, except if G is the complete bipartite graph K_{3 , 3} or the 5-prism C5□K2. Further they construct two infinite families of connected cubic graphs with independent domination three-eighths their order. In this paper, we provide a new family of connected cubic graphs G of order n such that i(G)=38n. We also show that if G is a subcubic graph of order n with no isolated vertex, then i(G)≤12n, and we characterize the graphs achieving equality in this bound.

Original language | English |
---|---|

Pages (from-to) | 28-41 |

Number of pages | 14 |

Journal | Journal of Combinatorial Optimization |

Volume | 43 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2022 |

## Keywords

- Cubic graph
- Independent domination
- Subcubic graph

## ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics