@@ -35,7 +35,7 @@ gap> IsDuplicateFree(DigraphEdges(D));
3535false
3636gap> IsMultiDigraph(D);
3737true
38- gap> D := DigraphMutableCopy(D);
38+ gap> D := DigraphMutableCopy(D);
3939<mutable multidigraph with 3 vertices, 7 edges>
4040gap> IsMultiDigraph(D);
4141true]]> </Example >
@@ -233,7 +233,7 @@ false]]></Example>
233233 <Returns ><K >true</K > or <K >false</K >.</Returns >
234234 <Description >
235235 A connected digraph is <E >biconnected</E > if it is still connected (in the
236- sense of <Ref Prop =" IsConnectedDigraph" />) when any vertex is removed.
236+ sense of <Ref Prop =" IsConnectedDigraph" />) when any vertex is removed.
237237 If <A >D</A > has at least 3 vertices, then <C >IsBiconnectedDigraph</C >
238238 implies <Ref Prop =" IsBridgelessDigraph" />;
239239 see <Ref Attr =" ArticulationPoints" /> or <Ref Attr =" Bridges" /> for a more
@@ -252,7 +252,7 @@ false]]></Example>
252252 the digraph.
253253 <P />
254254
255- See also <Ref Attr =" Bridges" />, <Ref Attr =" ArticulationPoints" />, and
255+ See also <Ref Attr =" Bridges" />, <Ref Attr =" ArticulationPoints" />, and
256256 <Ref Prop =" IsBridgelessDigraph" />.
257257 <P />
258258
@@ -504,7 +504,7 @@ true]]></Example>
504504 Oper =" CycleDigraph" />.<P />
505505
506506 A digraph is a <E >cycle</E > if and only if it is strongly connected and has
507- the same number of edges as vertices.
507+ the same number of edges as vertices.
508508 <P />
509509
510510 &MUTABLE_RECOMPUTED_PROP;
@@ -1307,14 +1307,27 @@ true
13071307 (<Ref Prop =" IsLatticeDigraph" />) which is distributive. That is to say,
13081308 the functions <Ref Oper =" PartialOrderDigraphMeetOfVertices" /> and
13091309 <Ref Oper =" PartialOrderDigraphJoinOfVertices" /> distribute over each other.<P />
1310-
1311- Equivalently, a <E >distributive lattice digraph</E > is a < E > lattice digraph</ E >
1310+
1311+ Equivalently, a <E >distributive lattice digraph</E > is a lattice digraph
13121312 in which the <E >lattice digraphs</E > representing <M >M3</M > and <M >N5</M > are
13131313 not embeddable as lattices
13141314 (see <URL >https://en.wikipedia.org/wiki/Distributive_lattice</URL > and
1315- <Ref Prop =" IsLatticeEmbedding"
1315+ <Ref Oper =" IsLatticeEmbedding"
13161316 Label =" for digraphs and a permutation or transformation" />).<P />
13171317
1318+ <Alt Only =" HTML" >
1319+ <![CDATA[
1320+ <figure>
1321+ <center>
1322+ <img height="200" src="m3.png"/>
1323+
1324+ <img height="200" src="n5.png"/>
1325+ <figcaption><p>The lattices <e>M3</e> and <e>N5</e>.</p></figcaption>
1326+ </center>
1327+ </figure>
1328+ <br/>
1329+ ]]>
1330+ </Alt >
13181331 &MUTABLE_RECOMPUTED_PROP;
13191332
13201333 <Example ><![CDATA[
@@ -1342,12 +1355,25 @@ false]]></Example>
13421355 <C >IsModularLatticeDigraph</C > returns <K >true</K > if the digraph
13431356 <A >digraph</A > is a <E >modular lattice digraph</E >.<P />
13441357
1345- A <E >modular lattice digraph</E > is a <E >lattice digraph</E >
1346- (<Ref Prop =" IsLatticeDigraph" />) which is modular. That is to say,
1347- the <E >lattice digraph</E > representing <M >N5</M > is not
1348- embeddable as a lattice
1358+ A <E >modular lattice digraph</E > is a lattice digraph (<Ref
1359+ 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
13491361 (see <URL >https://en.wikipedia.org/wiki/Modular_lattice</URL > and
1350- <Ref Prop =" IsLatticeEmbedding" />).
1362+ <Ref Oper =" IsLatticeEmbedding"
1363+ Label =" for digraphs and a permutation or transformation" />).<P />
1364+
1365+ <Alt Only =" HTML" >
1366+ <![CDATA[
1367+ <figure>
1368+ <center>
1369+ <img height="200" src="n5.png"/>
1370+
1371+ <figcaption><p>The lattice <e>N5</e>.</p></figcaption>
1372+ </center>
1373+ </figure>
1374+ <br/>
1375+ ]]>
1376+ </Alt >
13511377
13521378 &MUTABLE_RECOMPUTED_PROP;
13531379
@@ -1468,7 +1494,7 @@ true
14681494 <Returns ><K >true</K > or <K >false</K >.</Returns >
14691495 <Description >
14701496 A connected digraph is <E >bridgeless</E > if it is still connected (in the
1471- sense of <Ref Prop =" IsConnectedDigraph" />) when any edge is removed.
1497+ sense of <Ref Prop =" IsConnectedDigraph" />) when any edge is removed.
14721498 If <A >digraph</A > has at least 3 vertices, then <Ref
14731499 Prop =" IsBiconnectedDigraph" /> implies <C >IsBridgelessDigraph</C >;
14741500 see <Ref Attr =" ArticulationPoints" /> or <Ref Attr =" Bridges" /> for a more
@@ -1487,7 +1513,7 @@ true
14871513 the digraph.
14881514 <P />
14891515
1490- See also <Ref Attr =" Bridges" />, <Ref Attr =" ArticulationPoints" />, and
1516+ See also <Ref Attr =" Bridges" />, <Ref Attr =" ArticulationPoints" />, and
14911517 <Ref Prop =" IsBiconnectedDigraph" />. <P />
14921518
14931519 &MUTABLE_RECOMPUTED_PROP;
@@ -1544,7 +1570,7 @@ true
15441570 of <C >a</C > and <C >b</C > covers <C >b</C >. <E >Lower semimodularity</E > is
15451571 defined analogously. <P />
15461572
1547- See also <Ref Prop =" IsLatticeDigraph" />, <Ref Oper =" NonUpperSemimodularPair" />,
1573+ See also <Ref Prop =" IsLatticeDigraph" />, <Ref Oper =" NonUpperSemimodularPair" />,
15481574 and <Ref Oper =" NonLowerSemimodularPair" />.
15491575
15501576 &MUTABLE_RECOMPUTED_PROP;
0 commit comments