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Add 2 images to doc
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doc/m3.png

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doc/n5.png

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doc/prop.xml

Lines changed: 41 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -35,7 +35,7 @@ gap> IsDuplicateFree(DigraphEdges(D));
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false
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gap> IsMultiDigraph(D);
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true
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gap> D := DigraphMutableCopy(D);
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gap> D := DigraphMutableCopy(D);
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<mutable multidigraph with 3 vertices, 7 edges>
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gap> IsMultiDigraph(D);
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true]]></Example>
@@ -233,7 +233,7 @@ false]]></Example>
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<Returns><K>true</K> or <K>false</K>.</Returns>
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<Description>
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A connected digraph is <E>biconnected</E> if it is still connected (in the
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sense of <Ref Prop="IsConnectedDigraph"/>) when any vertex is removed.
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sense of <Ref Prop="IsConnectedDigraph"/>) when any vertex is removed.
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If <A>D</A> has at least 3 vertices, then <C>IsBiconnectedDigraph</C>
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implies <Ref Prop="IsBridgelessDigraph"/>;
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see <Ref Attr="ArticulationPoints"/> or <Ref Attr="Bridges"/> for a more
@@ -252,7 +252,7 @@ false]]></Example>
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the digraph.
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<P/>
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See also <Ref Attr="Bridges"/>, <Ref Attr="ArticulationPoints"/>, and
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See also <Ref Attr="Bridges"/>, <Ref Attr="ArticulationPoints"/>, and
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<Ref Prop="IsBridgelessDigraph"/>.
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<P/>
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@@ -504,7 +504,7 @@ true]]></Example>
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Oper="CycleDigraph"/>.<P/>
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A digraph is a <E>cycle</E> if and only if it is strongly connected and has
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the same number of edges as vertices.
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the same number of edges as vertices.
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<P/>
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&MUTABLE_RECOMPUTED_PROP;
@@ -1307,14 +1307,27 @@ true
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(<Ref Prop="IsLatticeDigraph"/>) which is distributive. That is to say,
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the functions <Ref Oper="PartialOrderDigraphMeetOfVertices"/> and
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<Ref Oper="PartialOrderDigraphJoinOfVertices"/> distribute over each other.<P/>
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Equivalently, a <E>distributive lattice digraph</E> is a <E>lattice digraph</E>
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Equivalently, a <E>distributive lattice digraph</E> is a lattice digraph
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in which the <E>lattice digraphs</E> representing <M>M3</M> and <M>N5</M> are
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not embeddable as lattices
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(see <URL>https://en.wikipedia.org/wiki/Distributive_lattice</URL> and
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<Ref Prop="IsLatticeEmbedding"
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<Ref Oper="IsLatticeEmbedding"
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Label="for digraphs and a permutation or transformation"/>).<P/>
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<Alt Only="HTML">
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<![CDATA[
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<figure>
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<center>
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<img height="200" src="m3.png"/>
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&nbsp;&nbsp;&nbsp;&nbsp;
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<img height="200" src="n5.png"/>
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<figcaption><p>The lattices <e>M3</e> and <e>N5</e>.</p></figcaption>
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</center>
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</figure>
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<br/>
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]]>
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</Alt>
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&MUTABLE_RECOMPUTED_PROP;
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<Example><![CDATA[
@@ -1342,12 +1355,25 @@ false]]></Example>
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<C>IsModularLatticeDigraph</C> returns <K>true</K> if the digraph
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<A>digraph</A> is a <E>modular lattice digraph</E>.<P/>
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1345-
A <E>modular lattice digraph</E> is a <E>lattice digraph</E>
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(<Ref Prop="IsLatticeDigraph"/>) which is modular. That is to say,
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the <E>lattice digraph</E> representing <M>N5</M> is not
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embeddable as a lattice
1358+
A <E>modular lattice digraph</E> is a lattice digraph (<Ref
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Prop="IsLatticeDigraph"/>) which is modular. That is to say, the <E>lattice
1360+
digraph</E> representing <M>N5</M> is not embeddable as a lattice
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(see <URL>https://en.wikipedia.org/wiki/Modular_lattice</URL> and
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<Ref Prop="IsLatticeEmbedding"/>).
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<Ref Oper="IsLatticeEmbedding"
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Label="for digraphs and a permutation or transformation"/>).<P/>
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<Alt Only="HTML">
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<![CDATA[
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<figure>
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<center>
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<img height="200" src="n5.png"/>
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1371+
<figcaption><p>The lattice <e>N5</e>.</p></figcaption>
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</center>
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</figure>
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<br/>
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]]>
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</Alt>
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&MUTABLE_RECOMPUTED_PROP;
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@@ -1468,7 +1494,7 @@ true
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<Returns><K>true</K> or <K>false</K>.</Returns>
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<Description>
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A connected digraph is <E>bridgeless</E> if it is still connected (in the
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sense of <Ref Prop="IsConnectedDigraph"/>) when any edge is removed.
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sense of <Ref Prop="IsConnectedDigraph"/>) when any edge is removed.
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If <A>digraph</A> has at least 3 vertices, then <Ref
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Prop="IsBiconnectedDigraph"/> implies <C>IsBridgelessDigraph</C>;
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see <Ref Attr="ArticulationPoints"/> or <Ref Attr="Bridges"/> for a more
@@ -1487,7 +1513,7 @@ true
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the digraph.
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<P/>
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1490-
See also <Ref Attr="Bridges"/>, <Ref Attr="ArticulationPoints"/>, and
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See also <Ref Attr="Bridges"/>, <Ref Attr="ArticulationPoints"/>, and
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<Ref Prop="IsBiconnectedDigraph"/>. <P/>
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&MUTABLE_RECOMPUTED_PROP;
@@ -1544,7 +1570,7 @@ true
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of <C>a</C> and <C>b</C> covers <C>b</C>. <E>Lower semimodularity</E> is
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defined analogously. <P/>
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1547-
See also <Ref Prop="IsLatticeDigraph"/>, <Ref Oper="NonUpperSemimodularPair"/>,
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See also <Ref Prop="IsLatticeDigraph"/>, <Ref Oper="NonUpperSemimodularPair"/>,
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and <Ref Oper="NonLowerSemimodularPair"/>.
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&MUTABLE_RECOMPUTED_PROP;

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