On the euclidean dimension of a wheel
Following Erdös, Harary, and Tutte, the euclidean dimension of a graphG is the minimumn such thatG can be embedded in euclideann-spaceR n so that each edge ofG has length 1. We present constructive proofs which give the euclidean dimension of a wheel and of a complete tripartite graph. We also define the generalized wheelWm,n as the join\(\bar K_m + C_n \) and determine the euclidean dimension of all generalized wheels.
KeywordsConstructive Proof Euclidean Dimension Tripartite Graph Complete Tripartite Graph Generalize Wheel
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- 1.Erdös, P.: On sets of distances ofn points in Euclidean space. Publ. Math. Inst. Hungar. Acad. Sci.5, 165–169 (1960)Google Scholar
- 2.Erdös, P., Harary, F., Tutte, W.T.: On the dimension of a graph. Mathematika12, 118–122 (1965)Google Scholar
- 3.Harary, F.: Graph Theory. Reading: Addison-Wesley 1969Google Scholar
- 4.Harary, F., Melter, R.: The graphs with no equilateral triangles. Gaz. Mat., Bucur.3, 182–183 (1982)Google Scholar