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Math 2.0

Combinatorics Example

Path graph

Example

Let $n \ge 1$ be an integer. The path graph $P_n$ is the graph with vertex set $\{0, 1, \dots, n - 1\}$ in which $i$ and $j$ are adjacent if and only if $|i - j| = 1$ .

Remarks

$P_n$ has $n$ vertices and $n - 1$ edges. It is a tree, and for $n \ge 2$ it has exactly two leaves, $0$ and $n - 1$ . Some authors write $P_n$ for the path with $n$ edges, that is, with $n + 1$ vertices.

Further reading

Web https://en.wikipedia.org/wiki/Path_graph, lead section

About this page

Tag	`075WR6W3Y3`
URI	`m2://075WR6W3Y3`
Kind	example
Writing	W2 usable
MSC	05C38
Instance of	Graph
Same as	Wikidata Q917421 Wikipedia Path graph

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