Preprint Article Version 1 This version is not peer-reviewed

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 (doi: 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 (doi: 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.

Subject Areas

chromatic polynomial; chromatically equivalent; chromatically unique; necklace graph

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