Graphs and Combinatorics

, Volume 35, Issue 4, pp 881–912 | Cite as

Independent Domination in Bipartite Cubic Graphs

  • Christoph BrauseEmail author
  • Michael A. Henning
Original Paper


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 \(G\not \cong K_{3,3}\) is a connected, cubic, bipartite graph on n vertices, then \(i(G) \le \frac{4}{11}n\). 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 \(K_{2,3}\).


Domination Independent Domination Cubic Graphs 

Mathematics Subject Classification




The authors express their sincere thanks to the referees for their meticulous and thorough reading of the paper.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Discrete Mathematics and AlgebraTU Bergakademie FreibergFreibergGermany
  2. 2.Department of Mathematics and Applied MathematicsUniversity of JohannesburgAuckland ParkSouth Africa

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