Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first
been investigated by Graham and Pollak Bell System Tech. J., 50 (1971), pp. 2495–2519
and Djoković J. Combinatorial Theory Ser. B, 14 (1973), pp. 263–267. Several papers
followed with various characterizations of partial cubes. In this paper, it is proven that a
subdivision of a complete graph of order n (n≧4) is a partial cube if and only if it is
isomorphic to S(K_n) or there exist n-1 nonsubdivided edges of K_n adjacent to a common …

Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first
been investigated by Graham and Pollack [RL Graham, H. Pollack On the addressing
problem for loop switching, Bell System Technol., J. 50 (1971) 2495–2519], and Djokovic̀ [D.
Djokovic̀, Distance preserving subgraphs of the hypercubes, Journal of Combinatorial
Theory, Ser B41 (1973), 263–267]. Several papers followed with various characterizations of
partial cubes. In this paper, we prove that a subdivision of a complete graph of order n (n⩾ …