GraphTheory - Maple Programming Help

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GraphTheory

 HighlightVertex
 highlight a vertex of a graph

 Calling Sequence HighlightVertex(G, V) HighlightVertex(G, V, C, ip) HighlightVertex(G, V, stylesheet=[ optionsequence ], ip )

Parameters

 G - graph V - a single vertex or a list, set, or Array of vertices of G C - (optional) color or list of colors ip - (optional) equation of the form inplace = true or inplace = false stylesheet - (optional) optionsequence is a sequence of keyword options to specify the style or a list of such sequences.

Description

 • By default the DrawGraph command draws the edges and vertices of the graph with the same set of style options. The command HighlightVertex, allows you to specify individual styles for specified vertices overriding the default or a previously set style.
 • Given only a graph G and a vertex or vertices V, HighlightVertex marks the specified vertices to be rendered with the default highlight style.
 • The simplest way to customize the rendering is to give C, a color for the vertex. The colors C can be given in any form understood by Maple. See ColorTools/Formats for details. When the color of the vertex is set the color of the vertex label is set automatically to an appropriately contrasting grayscale.
 • If V is a list or Array of vertices then a list of colors or stylesheets is used to associate a different color or style to each member.
 • By default, this command modifies G and returns nothing. If you supply the option inplace = false, then instead the changes are applied to a copy of G, and that copy is returned.
 • More precise control of the style can be set using stylesheet options. The stylesheet options are understood as modifiers to the default highlight style. So, for example, if a color is not specified the default highlight color is used. If the stylesheet option and a color C are both given, the color C is ignored.

Vertex Stylesheet Options

 • The styles that are understood for vertices are:
 – border : whether to draw the border, true or false
 – color : color of the vertex. See ColorTools/Format
 – fontcolor : color of the vertex label. See ColorTools/Format
 – fontsize : size of the vertex label, a positive integer in points
 – fontfamily : font family to use for the vertex label, a string. See plot/options
 – fontstyle : font style to use for the vertex label, a string. See plot/options
 – font : shorthand to specify a vertex label font as a list either [family, size] or [family, style, size]
 – padding : extra space around vertex label, a number in points
 – shape : shape of the vertex, a string understood by plottools/polygonbyname or default.  Examples:
 • ellipse, circle,
 • common polygons up to ten sides e.g. hexagon
 • arbitrary regular polygons given as number-gon e.g. 7gon
 • a regular star version of polygons with more than 4 sides will be drawn if prefixed (with or without spaces) with star e.g. star hexagon
 • a flattened version of a polygon will be drawn if prefixed with wide e.g. wide pentagon
 • the wide and star prefixes can be combined in any order
 • polygons are drawn with a flat bottom unless prefixed with inverted in which case it will have point bottom e.g. inverted 9gon
 • the inverted, star, and wide prefixes can be combined, but inverted must come first, though it can be abbreviated to inv,  e.g. invwide13gon
 – thickness : thickness of the border, a nonnegative value

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{K5}≔\mathrm{CompleteGraph}\left(5\right)$
 ${\mathrm{K5}}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 5 vertices and 10 edge\left(s\right)}}$ (1)

The default highlight style

 > $\mathrm{HighlightVertex}\left(\mathrm{K5},1\right)$
 > $\mathrm{DrawGraph}\left(\mathrm{K5}\right)$

Highlight using a custom color

 > $\mathrm{HighlightVertex}\left(\mathrm{K5},\left\{1,3\right\},"DodgerBlue"\right)$
 > $\mathrm{DrawGraph}\left(\mathrm{K5}\right)$

Highlighting vertices a second time does not merge styles but overwrites them.

 > $\mathrm{HighlightVertex}\left(\mathrm{K5},\left\{1,3\right\},\mathrm{stylesheet}=\left[\mathrm{font}=\left["Courier","bold",14\right],\mathrm{thickness}=3\right]\right)$
 > $\mathrm{DrawGraph}\left(\mathrm{K5}\right)$
 > $G≔\mathrm{Graph}\left(\left\{\left\{1,2\right\},\left\{2,3\right\},\left\{3,1\right\},\left\{3,4\right\},\left\{4,5\right\},\left\{5,6\right\},\left\{6,4\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 6 vertices and 7 edge\left(s\right)}}$ (2)
 > $A≔\mathrm{ArticulationPoints}\left(G\right)$
 ${A}{≔}\left[{3}{,}{4}\right]$ (3)
 > $H≔\mathrm{HighlightVertex}\left(G,A,\mathrm{stylesheet}=\left[\mathrm{color}="Magenta",\mathrm{border}=\mathrm{false},\mathrm{fontstyle}="bold"\right],\mathrm{inplace}=\mathrm{false}\right)$
 ${H}{≔}{\mathrm{Graph 3: an undirected unweighted graph with 6 vertices and 7 edge\left(s\right)}}$ (4)
 > $\mathrm{DrawGraph}\left(H\right)$

G was unchanged

 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{HighlightVertex}\left(G,\left[1,5\right],\left["Fill Spring Blue","Fill Spring Yellow"\right]\right)$
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{HighlightVertex}\left(G,\left[2,3\right],\mathrm{stylesheet}=\left[\left[\mathrm{fontstyle}="italic"\right],\left[\mathrm{fontstyle}="bold"\right]\right]\right)$
 > $\mathrm{DrawGraph}\left(G\right)$

Compatibility

 • The GraphTheory[HighlightVertex] command was updated in Maple 2019.
 • The stylesheet option was updated in Maple 2019.