A graph G is k-geodetically connected (k-GC) 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. We completely characterize the class of minimum 3-GC graphs that have the fewest edges for
Geodetic connectivity of graphs
β Scribed by Entringer, R.; Jackson, D.; Slater, P.
- Book ID
- 117913922
- Publisher
- IEEE
- Year
- 1977
- Weight
- 547 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0098-4094
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π SIMILAR VOLUMES
Let G = ( y E) be a graph with vertex set V of size n and edge set E of size m. A vertex LJ E V is called a hinge vertex if the distance of any two vertices becomes longer after u is removed. A graph without hinge vertex is called a hinge-free graph. In general, a graph G is k-geodetically connected
A graph can be metrized by assigning a length to each of its edges. Such a graph is said to be geodetic if for each pair of vertices there is a unique geodesic joining them. It is said to be normally geodetic if each of these unique geodesics is one of the geodesics in the usual metrization of the g