Geodesic
Spherical and clockwise spherical graphs
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 295-309
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The main subject of our study are spherical (weakly spherical) graphs, i.e. connected graphs fulfilling the condition that in each interval to each vertex there is exactly one (at least one, respectively) antipodal vertex. Our analysis concerns properties of these graphs especially in connection with convexity and also with hypercube graphs. We deal e.g. with the problem under what conditions all intervals of a spherical graph induce hypercubes and find a new characterization of hypercubes: $G$ is a hypercube if and only if $G$ is spherical and bipartite.
The main subject of our study are spherical (weakly spherical) graphs, i.e. connected graphs fulfilling the condition that in each interval to each vertex there is exactly one (at least one, respectively) antipodal vertex. Our analysis concerns properties of these graphs especially in connection with convexity and also with hypercube graphs. We deal e.g. with the problem under what conditions all intervals of a spherical graph induce hypercubes and find a new characterization of hypercubes: $G$ is a hypercube if and only if $G$ is spherical and bipartite.
Classification : 05C12, 05C65, 05C75
Keywords: spherical graph; hypercube; antipodal vertex; interval 
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Berrachedi, Abdelhafid; Havel, Ivan; Mulder, Henry Martyn. Spherical and clockwise spherical graphs. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 295-309. http://geodesic.mathdoc.fr/item/CMJ_2003_53_2_a6/

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