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Chromatic Polynomial and Chromatic Uniqueness of Necklace Graph
Version 1
: Received: 16 August 2018 / Approved: 17 August 2018 / Online: 17 August 2018 (11:24:33 CEST)
How to cite: Ali, U.; Bokhary, S. A. U. H.; Ashraf, S. Chromatic Polynomial and Chromatic Uniqueness of Necklace Graph. Preprints 2018, 2018080299. https://doi.org/10.20944/preprints201808.0299.v1 Ali, U.; Bokhary, S. A. U. H.; Ashraf, S. Chromatic Polynomial and Chromatic Uniqueness of Necklace Graph. Preprints 2018, 2018080299. https://doi.org/10.20944/preprints201808.0299.v1
Abstract
For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph Nn, for n ≥ 2 has been determined. It is further shown that N3 is chromatically unique.
Keywords
chromatic polynomial; chromatically equivalent; chromatically unique; necklace graph
Subject
Physical Sciences, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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