Spherical and Clockwise Spherical Graphs |
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Authors: | Abdelhafid Berrachedi Ivan Havel Henry Martyn Mulder |
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Institution: | (1) Institut de mathématiques, USTHB, BP 32, Alger, Algérie;(2) Academy of Sciences of the Czech Republic, itná 25, Mathematical Institute, 115 67 Praha 1, Czech Republic;(3) Econometrisch Instituut, Erasmus Universiteit, 3000 DR Rotterdam, Netherlands |
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Abstract: | 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. |
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Keywords: | spherical graph hypercube antipodal vertex interval |
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