CrownGraph - Maple Help

GraphTheory[SpecialGraphs]

 CrownGraph
 construct crown graph

 Calling Sequence CrownGraph(n) CrownGraph(L1, L2)

Parameters

 n - positive integer L1, L2 - lists of vertices; length of lists must be equal

Description

 • The CrownGraph(n) function creates the crown graph on 2n vertices.
 • The crown graph is a bipartite graph with vertices $\left[{u}_{1},\mathrm{...},{u}_{n},{v}_{1},\mathrm{...},{v}_{n}\right]$ in which an edge exists between $\left[{u}_{i}\right]$ and ${v}_{j}$ whenever i differs from j.
 • A crown graph with 2n vertices has $n\left(n-1\right)$ edges.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{CrownGraph}\left(5\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 10 vertices and 20 edge\left(s\right)}}$ (1)
 > $\mathrm{Edges}\left(G\right)$
 $\left\{\left\{{1}{,}{4}\right\}{,}\left\{{1}{,}{6}\right\}{,}\left\{{1}{,}{8}\right\}{,}\left\{{1}{,}{10}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{2}{,}{5}\right\}{,}\left\{{2}{,}{7}\right\}{,}\left\{{2}{,}{9}\right\}{,}\left\{{3}{,}{6}\right\}{,}\left\{{3}{,}{8}\right\}{,}\left\{{3}{,}{10}\right\}{,}\left\{{4}{,}{5}\right\}{,}\left\{{4}{,}{7}\right\}{,}\left\{{4}{,}{9}\right\}{,}\left\{{5}{,}{8}\right\}{,}\left\{{5}{,}{10}\right\}{,}\left\{{6}{,}{7}\right\}{,}\left\{{6}{,}{9}\right\}{,}\left\{{7}{,}{10}\right\}{,}\left\{{8}{,}{9}\right\}\right\}$ (2)
 > $\mathrm{DrawGraph}\left(G\right)$

Compatibility

 • The GraphTheory[SpecialGraphs][CrownGraph] command was introduced in Maple 2021.
 • For more information on Maple 2021 changes, see Updates in Maple 2021.