StarGraph

The star graph on $n$ vertices — one centre joined to $n - 1$ leaves.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageStarGraph✓↗

StarGraph(n)vertex 1 is the centre, joined to vertices $2, \dots, n$.

SageMathenumeratio_graph(graphs.StarGraph(n - 1))

Typed signatures

Type	Package	Applies
(integer) -> value	combinatorics	always

Domain: Collections

Examples

Basic #

The centre of a 6-vertex star has degree 5

live ↗

In$\mathrm{VertexDegree}(\mathrm{StarGraph}(6), 1)$Out$5$

Scope #

One hub joined to seven leaves

live ↗

In$\mathrm{StarGraph}(8)$Out$\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4, 5, 6, 7, 8\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(1, 3), \mathrm{UndirectedEdge}(1, 4), \mathrm{UndirectedEdge}(1, 5), \mathrm{UndirectedEdge}(1, 6), \mathrm{UndirectedEdge}(1, 7), \mathrm{UndirectedEdge}(1, 8)\bigr\rbrack)$

A hub with five spokes

live ↗

In$\mathrm{StarGraph}(6)$Out$\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(1, 3), \mathrm{UndirectedEdge}(1, 4), \mathrm{UndirectedEdge}(1, 5), \mathrm{UndirectedEdge}(1, 6)\bigr\rbrack)$

Applications #

The hub reaches everything in one step; each leaf needs two

live ↗

In$\mathrm{Map}(\operatorname{\_1}↦\mathrm{VertexEccentricity}(\mathrm{StarGraph}(6), \operatorname{\_1}), \mathrm{VertexList}(\mathrm{StarGraph}(6)))$Out$\bigl\lbrack1, 2, 2, 2, 2, 2\bigr\rbrack$

Properties #

A star is a tree

live ↗

In$\mathrm{IsTreeGraph}(\mathrm{StarGraph}(5))$Out$\mathrm{True}$

Hub on one side, leaves on the other

live ↗

In$\mathrm{IsBipartiteGraph}(\mathrm{StarGraph}(5))$Out$\mathrm{True}$

A hub joined to six leaves

live ↗

In$\mathrm{StarGraph}(7)$Out$\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4, 5, 6, 7\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(1, 3), \mathrm{UndirectedEdge}(1, 4), \mathrm{UndirectedEdge}(1, 5), \mathrm{UndirectedEdge}(1, 6), \mathrm{UndirectedEdge}(1, 7)\bigr\rbrack)$

About

Examples	7
Checked against	Wolfram Language 7 agreeSageMath 3 agree3 differ
Crosswalk	Wolfram LanguageSageMath

Implementation

mappedsagepackages/oracle/src/mappings.ts

See also: PathGraph, CompleteKaryTree