zbMATH — the first resource for mathematics

Criticality concepts in geodetic graphs. (English) Zbl 0614.05029
A graph is said to be geodetic if any pair of its vertices is connected by a unique shortest path. The author proves that if G is a geodetic block then G-\(e(G+e)\) is not geodetic for any edge e of G (for any new edge e).
Reviewer: P.Horák

05C38 Paths and cycles
05C35 Extremal problems in graph theory
Full Text: EuDML
[1] BOSÁK J.: Geodetic graphs. Combinatorics (Proc. Colloq. Keszthely) 1978, 151-172. · Zbl 0383.05024
[2] HARARY R.: Graph Theory. Addison-Wesley, Reading, Mass., 1969. · Zbl 0196.27202
[3] PARTHASARATHY K. R., SRINIVASAN N.: Some general constructions of geodetic blocks. J. Combin. Th. Ser. B, 33, 1982, 121-136. · Zbl 0488.05056
[4] PARTHASARATHY K. R., SRINIVASAN N.: Geodetic blocks of diameter three, Combinatorica 4 (2-3). 1984, 197-206. · Zbl 0554.05043
[5] PLESNÍK J.: A construction of geodetic graphs based on pulling subgraph homeomorphic to complete graphs. J. Combin. Theory Ser. B 36, 1984, 284-297. · Zbl 0527.05043
[6] SRINIVASAN N.: A study of geodetic graphs. Dissertation, The Indian Institute of Technology, Madras, 1982.
[7] STEMPLE J. G., WATKINS M. E.: On planar geodetic graphs. J. Combin. Th., 4, 1968, 101-117. · Zbl 0153.54004
[8] STEMPLE J. G.: Geodetic graphs homeomorphic to a complete graph. Annals of New York Academy of Sciences, Vol. 319, New York Academy of Sciences, New York, 1979, 512-517. · Zbl 0481.05057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.