, Volume 4, Issue 1, pp 23-30

On the euclidean dimension of a wheel

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Abstract

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 wheelW m,n as the join \(\bar K_m + C_n \) and determine the euclidean dimension of all generalized wheels.