## Abstract

A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the minimum cardinality of an independent dominating set. In this talk, we study the following conjecture posed by Goddard and Henning [Discrete Math. 313 (2013), 839-854]: If G 6= K_{3,3} is a connected, cubic, bipartite graph on n vertices, then i(G) = _{11}^{4} n. As a consequence of a more general result due to Dorbec et al. [J. Graph Theory 80(4) (2015), 329-349], it is known that if G is a bipartite, connected, cubic, graph of order n that does not have an induced subgraph isomorphic to a supergraph of K_{2,3}, then i(G) = ^{3}_{8}n. In this talk, we improve this ^{3}_{8}-upper bound to a _{11}^{4} -upper bound, thereby proving the Goddard-Henning conjecture when the graph does not have an induced subgraph isomorphic to a supergraph of K_{2,3}. This strengthens a result in [Discrete Applied Math. 162 (2014), 399-403] which proves the Goddard-Henning conjecture when the girth is at least 6.

Original language | English |
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Pages | 19-22 |

Number of pages | 4 |

Publication status | Published - 2020 |

Event | 15th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2017 - Cologne, Germany Duration: 6 Jun 2017 → 8 Jun 2017 |

### Conference

Conference | 15th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2017 |
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Country/Territory | Germany |

City | Cologne |

Period | 6/06/17 → 8/06/17 |

## ASJC Scopus subject areas

- Control and Optimization
- Discrete Mathematics and Combinatorics