The geodetic number of a graph
โ Scribed by Frank Harary; Emmanuel Loukakis; Constantine Tsouros
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 406 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For two vertices u and v of an oriented graph D, the set I (u, v) consists of all vertices lying on a uv geodesic or vu geodesic in D. If S is a set of vertices of D, then I (S) is the union of all sets I (u, v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the
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
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
We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.
We develop further the communication overlap index of Hong and Zuo in the case where the points of the graph communicate with each other through shortest paths (geodesics) of the graph. The structure of the graphs with minimum geodetic communication index is described, the concept of geodetic connec