The search for chromatically unique graphs

“…[13]); (2) G and H has the same girth and the same number of cycles with length equal to their girth (see [14]); (3) If G is a K 4 -homeomorph, then H must itself be a K 4 -homeomorph (see [15]…”

Section: Preliminary Resultsmentioning

confidence: 99%

Chromaticity of a family of K4-homeomorph with Girth 9

Karim¹,

Hasni²,

Lau³

2014

AIP Conference Proceedings

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Abstract. For a graph G, let P(G,λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ-equivalent), denoted by G ~ H, if P(G,λ) = P (H,λ). A graph G is chromatically unique (or simply χ-unique) if for any graph H such as H ~ G, we have H G, i.e, H is isomorphic to G. A K 4 -homeomorph is a subdivision of the complete graph K 4 . In this paper, we investigate the chromaticity of one family of K 4 -homeomorph which has girth 9, and give sufficient and necessary condition for the graph in the family to be chromatically unique.

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“…, a k ) to be chromatically unique? Many papers [4,5,16,17] have been published on this problem, but it is still far from being completely solved.…”

Section: Introductionmentioning

confidence: 99%