## Abstract A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each
An algebraic characterization of geodetic graphs
✍ Scribed by Ladislav Nebeský
- Book ID
- 110419960
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 339 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0011-4642
No coin nor oath required. For personal study only.
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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