We show that for each k L 4 there exists a connected k-domination critical graph with independent domination number exceeding k, thus disproving a conjecture of Sumner and Blitch ( J Cornbinatorial Theory B 34 (19831, 65-76) in all cases except k = 3.
On graphs with equal domination and independent domination numbers
โ Scribed by Jerzy Topp; Lutz Volkmann
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 284 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
Topp, J. and L. Volkmann, On graphs wi',h equal domination and independent domination number, Discrete Mathematics 96 (1991) 75-80.
Allan and Laskar have shown that Kt.s-free graphs are graphs with equal domination and independent domination numbers. In this paper new classes of graphs with equal domination and independent domination numbers are presented. In particular, the result of Allan and Laskar is generalized.
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