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`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 |

Appears in Collections: | Staff Publications |

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