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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     author = {Wenhua Lan and Xiang Lin Wei},
     title = {Classification of {Seven-Point} {Four-Distance} {Sets} in the {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {492--508},
     publisher = {mathdoc},
     volume = {93},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a1/}
}
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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/