Minimum 3-geodetically connected graphs. (English) Zbl 1029.05045
A graph \(G\) is \(k\)-geodetically connected if it is connected and the removal of at least \(k\) vertices is required to increase the distance between at least one pair of vertices or reduce \(G\) to a single vertex. The author characterizes the class of minimum 3-geodetically connected graphs that have the fewest edges for a given number of vertices.
Reviewer: Alexander Rappoport (Moskva)
MSC:
| 05C12 | Distance in graphs |
| 05C35 | Extremal problems in graph theory |
| 05C38 | Paths and cycles |
| 05C40 | Connectivity |
| 05C75 | Structural characterization of families of graphs |
References:
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| [2] | Entringer, R. E.; Jackson, D. E.; Slater, P. J., Geodetic connectivity of graphs, IEEE Trans. Circuits and Systems, CAS-24, 460-463 (1977) · Zbl 0344.05137 |
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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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
