All Outputs (3)

The k-tuple domination number revisited (2008)
Journal Article
Zverovich, V. (2008). The k-tuple domination number revisited. Applied Mathematics Letters, 21(10), 1005-1011. https://doi.org/10.1016/j.aml.2007.10.016

The following fundamental result for the domination number γ (G) of a graph G was proved by Alon and Spencer, Arnautov, Lovász and Payan: γ (G) ≤ frac(ln (δ + 1) + 1, δ + 1) n, where n is the order and δ is the minimum degree of vertices of G. A simi... Read More about The k-tuple domination number revisited.

Upper bounds for the alpha-domination number (2008)
Presentation / Conference
Gagarin, A., Poghosyan, A., & Zverovich, V. (2008, May). Upper bounds for the alpha-domination number. Presented at The 4th East Cost Combinatorial Conference, Canada

A generalised upper bound for the k-tuple domination number (2008)
Journal Article
Gagarin, A., & Zverovich, V. (2008). A generalised upper bound for the k-tuple domination number. Discrete Mathematics, 308(5-6), 880-885. https://doi.org/10.1016/j.disc.2007.07.033

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G,γ× k (G) ≤ frac(ln (δ - k + 2) + ln (∑m = 1k - 1 (k - m) over(d... Read More about A generalised upper bound for the k-tuple domination number.