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This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a result, the enumeration of the class of geodetic graphs homeomorphic to certain Moore graphs has been performed.
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An undirected graph G = (V;E) is said to be geodetic, if between any pair of vertices x; y 2 V there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are de ned as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k{geodetic graphs are studied.
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ژورنال
عنوان ژورنال: Geophysical Journal of the Royal Astronomical Society
سال: 2007
ISSN: 0016-8009
DOI: 10.1111/j.1365-246x.1971.tb01804.x