1. Independent Domination in Bipartite Cubic Graphs.
- Author
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Brause, Christoph and Henning, Michael A.
- Subjects
DOMINATING set ,BIPARTITE graphs ,INDEPENDENT sets ,MATHEMATICS ,LOGICAL prediction ,GEODESICS - 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 paper, we study the following conjecture posed by Goddard and Henning (Discrete Math. 313:839–854, 2013): If G ≇ K 3 , 3 is a connected, cubic, bipartite graph on n vertices, then i (G) ≤ 4 11 n . Henning et al. (Discrete Appl. Math. 162:399–403, 2014) prove the conjecture when the girth is at least 6. In this paper we strengthen this result by proving the conjecture when the graph has no subgraph isomorphic to K 2 , 3 . [ABSTRACT FROM AUTHOR]
- Published
- 2019
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