Abstract
We study the question as to the extent to which the size id(G) of a minimum independent dominating set of a graph G can differ from the size d(G) of a minimum dominating set of G under some restrictions on the vertex degrees in G. We obtain upper bounds for the ratio id(G)/d(G) for graphs with a given maximum degree and for regular graphs of a given degree.
The research of the first author was partially supported by the Russian Foundation for Fundamental Research (Grant 93–01–00489); the research of the second author was partially supported by the Russian Foundation for Fundamental Research (Grant 93–01–01486) and the International Science Foundation (Grant RPY000).
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References
R. B. Allan and R. Laskar (1978) On domination and independent domination numbers of a graph, Discrete Math. 23, 73–76.
C. Barefoot, F. Harary, and K. F. Jones (1991) What is the difference between domination and independent domination numbers of a cubic graph? Graphs Combin. 7, No. 1, 205–208.
A. V. Kostochka (1993) The independent domination number of a cubic 3-con-nected graph can be much larger than its domination number, Graphs Combin. 9, No. 3, 235–237.
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© 1996 Kluwer Academic Publishers
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Glebov, N.I., Kostochka, A.V. (1996). On Minimum Independent Dominating Sets in Graphs. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_5
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DOI: https://doi.org/10.1007/978-94-009-1606-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7217-5
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