Path graph
This article is about a family of graphs. For paths as parts of arbitrary graphs, see Path (graph theory).
Not to be confused with line graph.
| Path graph | |
|---|---|
|
A path graph on 6 vertices | |
| Vertices | n |
| Edges | n - 1 |
| Radius | ⌊n/2⌋ |
| Diameter | n - 1 |
| Automorphisms | 2 |
| Chromatic number | 2 |
| Chromatic index | 2 |
| Spectrum | {2 cos(k π / (n + 1))1; k=1,...,n} |
| Properties |
Unit distance Bipartite graph Tree |
| Notation |
 |
In the mathematical field of graph theory, a path graph or linear graph is a particularly simple example of a tree, namely a tree with two or more vertices that is not branched at all, that is, contains only vertices of degree 2 and 1. In particular, it has two terminal vertices (vertices that have degree 1), while all others (if any) have degree 2.
Paths and cycles are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005).
See also
- Glossary of graph theory
- Path (graph theory)
- Caterpillar tree
- Complete graph
- Null graph
- Path decomposition
References
- Bondy, J. A.; Murty, U. S. R. (1976). Graph Theory with Applications. North Holland. pp. 12–21. ISBN 0-444-19451-7.
- Diestel, Reinhard (2005). Graph Theory (3rd ed. ed.). Graduate Texts in Mathematics, vol. 173, Springer-Verlag. pp. 6–9. ISBN 3-540-26182-6.