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Title: Spherical and clockwise spherical graphs (English)
Author: Berrachedi, Abdelhafid
Author: Havel, Ivan
Author: Mulder, Henry Martyn
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 2
Year: 2003
Pages: 295-309
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: spherical graph
Keyword: hypercube
Keyword: antipodal vertex
Keyword: interval
MSC: 05C12
MSC: 05C65
MSC: 05C75
idZBL: Zbl 1021.05085
idMR: MR1983453
Date available: 2009-09-24T11:01:44Z
Last updated: 2020-07-03
Stable URL:
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