Geodesic
Classification of Seven-Point Four-Distance Sets in the Plane
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 492-508.

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A point set $X$ in the plane is called a $k$-distance set if there are exactly $k$ different distances between two distinct points in $X$. In this paper, we classify $7$-point $4$-distance sets and show that there are forty two $7$-point $4$-distance sets in the plane up to isomorphism, we also give some results about diameter graphs.
Keywords: $n$-point $k$-distance set, diameter graph.
Mots-clés : isomorphism 
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     title = {Classification of {Seven-Point} {Four-Distance} {Sets} in the {Plane}},
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Wenhua Lan; Xiang Lin Wei. Classification of Seven-Point Four-Distance Sets in the Plane. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 492-508. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a1/

[1] P. Erdős, P. Fishburn, “Maximum planar sets that determine $k$ distances”, Discrete Math., 160:1-3 (1996), 115–125 | DOI | MR | Zbl

[2] M. Shinohara, “Classification of three-distance sets in two dimensional Euclidean space”, European J. Combin., 25:7 (2004), 1039–1058 | DOI | MR | Zbl

[3] M. Shinohara, “Uniqueness of maximum planar five-distance sets”, Discrete Math., 308:14 (2008), 3048–3055 | DOI | MR | Zbl

[4] P. Erdős, P. Fishburn, “Convex nonagons with five intervertex distances”, Geom. Dedicata, 60:3 (1996), 317–332 | MR | Zbl

[5] P. Fishburn, “Convex polygons with few intervertex distances”, Comput. Geom., 5:2 (1995), 65–93 | DOI | MR | Zbl

[6] Xianglin Wei, “Classification of eleven-point five-distance sets in the plane”, Ars Combin., 102 (2011), 505–515 | MR | Zbl