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- W40378616 abstract "Four kinds of dimensions μi(G) of a finite graph G are defined and studied, i = 1, 2, 3, 4. Dimension μ1 (G) is the “Sabidussi dimension” and μ2(G) coincides with the “isometric dimension” of G defined by R. L. Graham and P. M. Winkler. We list some properties of these dimensions and calculate their value in some particular cases: complete graphs, cycles, trees, (3,4)-connected graphs, and n-partite graphs Km1,m2….mn The dimension of a product is always the sum of those of the factors; this leads for instance to the value of the dimension of a hypercube and of an n-dimensional grid Pm1 ▪ Pm2 ▪ Pmn All proofs are omitted for shortness and can be found in [2], where some other results are also given." @default.
- W40378616 created "2016-06-24" @default.
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- W40378616 date "1992-01-01" @default.
- W40378616 modified "2023-09-27" @default.
- W40378616 title "Cartesian Dimensions of a Graph" @default.
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- W40378616 doi "https://doi.org/10.1016/s0167-5060(08)70605-8" @default.
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