Chromaticity of a family of K4-homeomorphs

Yan-ling, Peng; Liu, Ruying

doi:10.1016/s0012-365x(02)00268-6

Cited by 6 publications

(10 citation statements)

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“…So far, the chromaticity of K 4 -homeomorph with girth g, where 3 ≤ g ≤ 7 has been studied by many authors(see [1][2][3][4][5]). Also the study of the chromaticity of K 4 -homeomorph with at least two paths of length 1 has been fulfilled (see [2,[6][7][8]). Recently, Shi et al [9] studied the chromaticity of one family of K 4 -homeomorph with girth 8, i.e., K 4 (2,3,3,d,e,f).…”

Section: All Graphs Considered Here Are Simple Graphs For Such a Gramentioning

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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Section: All Graphs Considered Here Are Simple Graphs For Such a Gramentioning

confidence: 99%

Chromaticity of a family of K4-homeomorph with Girth 9

Karim¹,

Hasni²,

Lau³

2014

AIP Conference Proceedings

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“…Such a homeomorph is denoted by K 4 (a, b, c, d, e, f ) if the six edges of K 4 are replaced by the six paths of length a, b, c, d, e, f , respectively, as shown in Figure 1. So far, the chromaticity of K 4 -homeomorphs with girth g, where 3 ≤ g ≤ 9 has been studied by many authors (see [5,[9][10][11]18]). In 2004, Peng in [9] published her work on the chromaticity of K 4 -homeomorphs with girth six by considering her result on the chromatic equivalence pair K 4 (1, 2, 3, d, e, f ) and K 4 (1, 2, 3, d ′ , e ′ , f ′ ).…”

Section: Introductionmentioning

confidence: 99%

“…al in [6] summarized the above result. In 2008, Peng [11] investigated the chromatic uniqueness of K 4 (1, 3, 3, d, e, f ) with exactly one path of length one and with girth seven. She accomplished this, first by establishing the chromatic equivalence pair of K 4 (1, 3, 3, d, e, f ) and K 4 (1, 3, 3, d ′ , e ′ , f ′ ) in [12].…”

Section: Introductionmentioning

confidence: 99%

“…She accomplished this, first by establishing the chromatic equivalence pair of K 4 (1, 3, 3, d, e, f ) and K 4 (1, 3, 3, d ′ , e ′ , f ′ ) in [12]. She then solved the chromatic equivalence of such families of graphs (see [12][13][14]) and finally, in [11], she provided the necessary and sufficient condition for this type of K 4 -homeomorph to be chromatically unique. S. Catada-Ghimire et al in [1] investigated the chromaticity of one family of K 4 -homeomorph with girth 10.…”

Section: Introductionmentioning

confidence: 99%

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On chromatic equivalence of a pair of K4-homeomorphs

Catada-Ghimire¹,

Roslan²,

Peng³

2010

OpMath

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Let P (G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically euqivalent, denoted G ∼ H, if P (G, λ) = P (H, λ). We write [G] = {H|H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we discuss a chromatically equivalent pair of graphs in one family of K4-homeomorphs, K4(1, 2, 8, d, e, f). The obtained result can be extended in the study of chromatic equivalence classes of K4(1, 2, 8, d, e, f) and chromatic uniqueness of K4-homeomorphs with girth 11.

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“…So far, the chromaticity of K 4 -homeomorphs which have girth 3, 4, or 5 has been studied (see [2,4,5]). In this paper, we study the chromaticity of K 4 -homeomorphs which have girth 6.…”

Section: Introductionmentioning

confidence: 99%