# Path graph

To be distinguished from line graph.
Path graph
A path graph on 6 vertices
Vertices n
Edges n - 1
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 $P_n$

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).