Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.disc.2007.04.045
Title: Domination numbers and zeros of chromatic polynomials
Authors: Dong, F.M.
Koh, K.M. 
Keywords: Chromatic polynomial
Domination number
Splitting-closed family
Zero
Zero-free interval
Issue Date: 28-May-2008
Source: Dong, F.M., Koh, K.M. (2008-05-28). Domination numbers and zeros of chromatic polynomials. Discrete Mathematics 308 (10) : 1930-1940. ScholarBank@NUS Repository. https://doi.org/10.1016/j.disc.2007.04.045
Abstract: In this paper, we shall prove that if the domination number of G is at most 2, then P (G, λ) is zero-free in the interval (1, β), whereβ = 2 + frac(1, 6) root(12 sqrt(93) - 108, 3) - frac(1, 6) root(12 sqrt(93) + 108, 3) = 1.317672196 ...,and P (G, β) = 0 for some graph G with domination number 2. We also show that if Δ (G) ≥ v (G) - 2, then P (G, λ) is zero-free in the interval (1, β′), whereβ′ = frac(5, 3) + frac(1, 6) root(12 sqrt(69) - 44, 3) - frac(1, 6) root(12 sqrt(69) + 44, 3) = 1.430159709 ...,and P (G, β′) = 0 for some graph G with Δ (G) = v (G) - 2. © 2007 Elsevier B.V. All rights reserved.
Source Title: Discrete Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103158
ISSN: 0012365X
DOI: 10.1016/j.disc.2007.04.045
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