A Note on a Theorem of H. L. Abbott
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 79-81
Voir la notice de l'article provenant de la source Cambridge University Press
Let In be the graph of the unit n-dimensional cube. Its 2n vertices are all the n-tuples of zeros and ones, two vertices being adjacent (joined by an edge) if and only if they differ in exactly one coordinate. A path P in In is a sequence x 1, ..., x m of distinct vertices in In where x i is adjacent to x i+1 for 1 ≤ i ≤ m-1; P is a circuit if it is also true that x m and x 1 are adjacent. A path is Hamiltonian if it passes through all the vertices of In . Finally, for vertices x and y in In , we define d(x, y) to be the graph theorectic distance between x and y, i.e., the number of coordinates in which x and y differ.
Douglas, Robert J. A Note on a Theorem of H. L. Abbott. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 79-81. doi: 10.4153/CMB-1970-016-1
@article{10_4153_CMB_1970_016_1,
author = {Douglas, Robert J.},
title = {A {Note} on a {Theorem} of {H.} {L.} {Abbott}},
journal = {Canadian mathematical bulletin},
pages = {79--81},
year = {1970},
volume = {13},
number = {1},
doi = {10.4153/CMB-1970-016-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-016-1/}
}
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