{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "restart;\nread \"C: /Documents and Settings/G. Michael Guy/My Documents/My Website/My HTML /mathSite/vgraphs-coms.mpl\";" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#QarAdded~Commands:~LapG,~DegG,~SNF,~f SNF,~oSNF,~ofSNF,~gdunion,~NPath,~ModPath,~ParPath,~DisPaths,~SkipN,~K Rho,~LineGraph6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "path1:=NPath(4); #This is co rrect, but produces lots of crazy output." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&path1Gj+6#%\"xG6\"6$%&GRAPHG%\"1GE\\s2%'_EdgesG<&%#e 1G%#e2G%#e3G%#e4G%*_AncestorG=F(%&falseGE\\[l!%/_EconnectivityGF7%+_Ne ighborsG=F(F5E\\[l&\"\"\"<#\"\"#F=<$F;\"\"$F?<$F=\"\"%\"\"&<#FAFA<$F?F B%*_VerticesG<'F;F=F?FAFB%&_HeadG=F(F5E\\[l!%*_DaughterG=F(F5E\\[l!%+_ CountcutsGFM%+_EdgeIndexG=%*symmetricGF5E\\[l%6$F=F?<#F06$FAFB<#F26$F? FA<#F16$F;F=<#F/%)_EweightG=F(F5E\\[l%F1F;F0F;F/F;F2F;%)_VweightG=%'sp arseGF5E\\[l!%(_StatusG<#%'SIMPLEG%&_TailG=F(F5E\\[l!%._BicomponentsGF ao%*_EmaxnameG\"\"'%,_CounttreesGFdo%&_EndsG=F(F5E\\[l%F1<$F?FAF0<$F=F ?F/<$F;F=F2<$FAFB@=/9$F->-9!6#F-<\"/F^pFN>-Fap6#FN-%&tableG6#FP/F^pFG> -Fap6#FG-FipF(/F^pF^o>-Fap6#F^oF_q/F^pFZ>-Fap6#FZF_q/F^pFeo>-Fap6#FeoF _q/F^pFE>-Fap6#FEFcp/F^pFgn>-Fap6#Fgn-Fip6#Fin/F^pF3>-Fap6#F3F_q/F^pFJ >-Fap6#FJF_q/F^pF8>-Fap6#F8F_q/F^pF[o>-Fap6#F[o<#.F]o/F^pFbo>-Fap6#Fbo \"\"!O.-Fap6#9\"F(F(F(6#F\\t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "path1:=NPath(1): #This is better." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "draw(path1);" }}{PARA 13 "" 1 "" {GLPLOT2D 252 233 233 {PLOTDATA 2 "6(-%'POINTSG6#7$$\"\"\"\"\"!$F)F)-%%TEXTG6$7$$\"#7!\" \"F*Q\"16\"-F$6#7$$F1F)$!+:w1-T!#>-F,6$7$$!#7F1F8Q\"2F3-%'CURVESG6$7$F &F6-%'COLOURG6&%$RGBGF)$\"#5F1F)-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve \+ 3" "Curve 4" "Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "p ath2:=NPath(2):\ndraw(path2);" }}{PARA 13 "" 1 "" {GLPLOT2D 223 222 222 {PLOTDATA 2 "6+-%'POINTSG6#7$$\"\"\"\"\"!$F)F)-F$6#7$$!+0+++]!#5$ \"+NSDg')F0-%%TEXTG6$7$$!+0+++qF0F1Q\"26\"-F$6#7$$!+*)******\\F0$!+WSD g')F0-F46$7$$!+*)******pF0F@Q\"3F:-%'CURVESG6$7$F&F--%'COLOURG6&%$RGBG F)$\"#5!\"\"F)-F46$7$$\"#7FRF*Q\"1F:-FI6$7$F-F=FL-%*AXESSTYLEG6#%%NONE G" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" " Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "newPath:=gdunion(path1,pa th2); #This is WRONG must used []'s" }}{PARA 8 "" 1 "" {TEXT -1 150 "E rror, (in gdunion) invalid input: convert/Matrix expects its 1st argum ent, M, to be of type \{Matrix, array, list, Vector, Array\}, but rece ived path1\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "newPath:=gd union([path1,path2]):\ndraw(newPath);" }}{PARA 13 "" 1 "" {GLPLOT2D 253 259 259 {PLOTDATA 2 "60-%'POINTSG6#7$$\"\"\"\"\"!$F)F)-F$6#7$$\"+Q *p,4$!#5$\"+l^c5&*F0-%%TEXTG6$7$$\"+Q*p,4&F0F1Q\"26\"-F$6#7$$!+]*p,4)F 0$\"+9D&y(eF0-%'CURVESG6$7$F=7$$!+M*p,4)F0$!+PD&y(eF0-%'COLOURG6&%$RGB GF)$\"#5!\"\"F)-FC6$7$FF7$$\"+l*p,4$F0$!+c^c5&*F0FK-F46$7$$!+&*p,45!\" *F@Q\"3F:-F$6#FF-F46$7$$!+$*p,45FinFIQ\"4F:-F$6#FU-F46$7$$\"+l*p,4&F0F XQ\"5F:-F46$7$$\"#7FQF*Q\"1F:-FC6$7$F&F-FK-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2 " "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9 " "Curve 10" "Curve 11" "Curve 12" "Curve 13" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "compOfPath:=KRho(6,newPath):\ndraw(compOfPath); " }}{PARA 13 "" 1 "" {GLPLOT2D 251 258 258 {PLOTDATA 2 "6;-%'CURVESG6$ 7$7$$\"\"\"\"\"!$F*F*7$$\"+\"*******\\!#5$!+VSDg')F/-%'COLOURG6&%$RGBG F*$\"#5!\"\"F*-F$6$7$F'7$$F8F*$\"+&QKz*e!#>F2-%'POINTSG6#F'-F$6$7$F'7$ $!+2+++]F/$!+MSDg')F/F2-F$6$7$7$$\"+-+++]F/$\"+PSDg')F/7$$!+(*******\\ F/$\"+SSDg')F/F2-F$6$7$FOFGF2-FB6#FO-%%TEXTG6$7$$\"+-+++qF/FRQ\"26\"-F B6#FT-Fin6$7$$!+(*******pF/FWQ\"3F_o-FB6#F<-Fin6$7$$!#7F8F>Q\"4F_o-Fin 6$7$$\"#7F8F+Q\"1F_o-F$6$7$FOF,F2-F$6$7$FTF,F2-F$6$7$FOF " 0 "" {MPLTEXT 1 0 17 "DegG(compOfPath);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")![ " 0 "" {MPLTEXT 1 0 22 "adjacency(compOfPath);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABL EG6%\");h[A-%'MATRIXG6#7(7(\"\"!F,\"\"\"F-F-F-F+7(F-F-F,F,F-F-7(F-F-F, F,F,F-7(F-F-F-F,F,F-7(F-F-F-F-F-F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "LapG(compOfPath);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")3ZaA-%'MATRIXG6#7(7(!\"%\"\"!\"\"\"F.F.F.7(F-F,F.F.F .F.7(F.F.F,F-F.F.7(F.F.F-!\"$F-F.7(F.F.F.F-F,F.7(F.F.F.F.F.!\"&%'Matri xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "SNF(compOfPath);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"\"\"F$F$F$\"$g$\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fSNF(compOfPath);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"\"\"F$F$F$*()-%!G6#\"\"#\"\"$F$)-F(6#F+F*F$-F(6# \"\"&F$\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "oSNF(compOf Path);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"$g$" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "ofSNF(compOfPath);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#*()-%!G6#\"\"#\"\"$\"\"\")-F'6#F*F)F+-F'6#\"\"&F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "charpoly(compOfPath,t); #Th is is the characteristic polynomial of the _adjacency_ matrix." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"tG\"\"'\"\"\"F(*&\"#7F()F&\"\" %F(!\"\"*&\"#=F()F&\"\"$F(F-*&F1F()F&\"\"#F(F-*&F,F(F&F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "MyFamily:=_i->KRho(_i,NPath(_i-4)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)MyFamilyGj+6#%#_iG6\"6$%)operat orG%&arrowGF(-%%KRhoG6$9$-%&NPathG6#,&F/\"\"\"\"\"%!\"\"F(F(F(6#\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for i from 4 to 10 do\n i=oSNF(MyFamily(i));\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"%7 $F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"&7$F$\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/\"\"'7$F$\"#!*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"(7$F$\"$0)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\")7$F$\"%7&* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"*7$F$\"'/\"R\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/\"#57$F$\"(q/U#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "fromScratch:=graph(\{1,2,3,4\},\{\{1,2\},\{1,4\},\{1, 3\}\}):\ndraw(fromScratch);" }}{PARA 13 "" 1 "" {GLPLOT2D 246 270 270 {PLOTDATA 2 "6.-%'CURVESG6$7$7$$\"\"\"\"\"!$F*F*7$$!+3Q.^?!#>F(-%'COLO URG6&%$RGBGF*$\"#5!\"\"F*-%%TEXTG6$7$$\"#7F6F+Q\"16\"-%'POINTSG6#F,-F8 6$7$$!+-+++?!#5F(Q\"2F>-F@6#7$$F6F*$!+:w1-TF/-F86$7$$!#7F6FMQ\"3F>-F$6 $7$F'7$$\"+A95`hF/FLF0-F$6$7$F'FKF0-F@6#FX-F86$7$$\"+1+++?FGFLQ\"4F>-F @6#F'-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "KFive:=complete(5):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "draw(KFive);" }}{PARA 13 "" 1 "" {GLPLOT2D 252 223 223 {PLOTDATA 2 "67-%%TEXTG6$7$$\"#7!\"\"$\"\"! F+Q\"16\"-%'CURVESG6$7$7$$\"\"\"F+F*7$$!+M*p,4)!#5$!+PD&y(eF8-%'COLOUR G6&%$RGBGF+$\"#5F)F+-F/6$7$F27$$\"+l*p,4$F8$!+c^c5&*F8F;-F/6$7$F5FDF;- F/6$7$F27$$\"+Q*p,4$F8$\"+l^c5&*F8F;-%'POINTSG6#FO-F/6$7$7$$!+]*p,4)F8 $\"+9D&y(eF8FDF;-F/6$7$FOFZF;-FU6#F2-F/6$7$F2FZF;-FU6#FZ-F$6$7$$!+&*p, 45!\"*FgnQ\"3F--FU6#F5-F$6$7$$!+$*p,45FhoF9Q\"4F--FU6#FD-F$6$7$$\"+Q*p ,4&F8FRQ\"2F--F$6$7$$\"+l*p,4&F8FGQ\"5F--F/6$7$FOFDF;-F/6$7$FZF5F;-F/6 $7$FOF5F;-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cur ve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 1 8" "Curve 19" "Curve 20" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "draw(complete(2,3)); #Bipartite graph. Read maple command ?complete t o learn more" }}{PARA 13 "" 1 "" {GLPLOT2D 281 314 314 {PLOTDATA 2 "63 -%%TEXTG6$7$$\"#7!\"\"$\"\"!F+Q\"16\"-%'CURVESG6$7$7$$\"\"\"F+F*7$$!+M *p,4)!#5$!+PD&y(eF8-%'COLOURG6&%$RGBGF+$\"#5F)F+-F/6$7$F27$$\"+l*p,4$F 8$!+c^c5&*F8F;-%'POINTSG6#7$$\"+Q*p,4$F8$\"+l^c5&*F8-F/6$7$FL7$$!+]*p, 4)F8$\"+9D&y(eF8F;-FJ6#F2-F/6$7$F2FTF;-FJ6#FT-F$6$7$$!+&*p,45!\"*FWQ\" 3F--FJ6#F5-F$6$7$$!+$*p,45F_oF9Q\"4F--FJ6#FD-F$6$7$$\"+Q*p,4&F8FOQ\"2F --F$6$7$$\"+l*p,4&F8FGQ\"5F--F/6$7$FLFDF;-F/6$7$FLF5F;-%*AXESSTYLEG6#% %NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" " Curve 15" "Curve 16" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Thr eeCycle:=cycle(3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "draw( ThreeCycle);" }}{PARA 13 "" 1 "" {GLPLOT2D 274 253 253 {PLOTDATA 2 "6, -%%TEXTG6$7$$\"#7!\"\"$\"\"!F+Q\"16\"-%'CURVESG6$7$7$$\"\"\"F+F*7$$!+* )******\\!#5$!+WSDg')F8-%'COLOURG6&%$RGBGF+$\"#5F)F+-%'POINTSG6#F2-F/6 $7$7$$!+0+++]F8$\"+NSDg')F8F5F;-FB6#FG-F$6$7$$!+0+++qF8FJQ\"2F--FB6#F5 -F$6$7$$!+*)******pF8F9Q\"3F--F/6$7$F2FGF;-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2 " "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9 " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "anotherGraph:=KRho(7,g union(ParPath(7),NPath(6))):\nLapG(anotherGraph);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")W%zF#-%'MATRIXG6#7)7)!\"$\"\"!F-\"\"\"F. F.F-7)F-!\"#F-F-F.F-F.7)F-F-F0F-F-F.F.7)F.F-F-F0F-F-F.7)F.F.F-F-F0F-F- 7)F.F-F.F-F-F0F-7)F-F.F.F.F-F-F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "draw(anotherGraph);" }}{PARA 13 "" 1 "" {GLPLOT2D 316 299 299 {PLOTDATA 2 "69-%%TEXTG6$7$$\"#7!\"\"$\"\"!F+Q\"16\"-%'POI NTSG6#7$$\"+=!)*[B'!#5$\"+D[J=yF4-F$6$7$$\"+=!)*[B)F4F5Q\"2F--F/6#7$$! +R$4_A#F4$\"+A\"z#\\(*F4-F$6$7$$!+R$4_A%F4FBQ\"3F--F/6#7$$!+z')o4!*F4$ \"+#RP)QVF4-F$6$7$$!+o)o45\"!\"*FOQ\"4F--F$6$7$FT$!+!RP)QVF4Q\"5F--F/6 #7$$!+J$4_A#F4$!+C\"z#\\(*F4-F$6$7$$!+J$4_A%F4F]oQ\"6F--F/6#7$$\"+D!)* [B'F4$!+>[J=yF4-F$6$7$$\"+D!)*[B)F4FjoQ\"7F--F/6#7$FMFen-%'CURVESG6$7$ F1Fgo-%'COLOURG6&%$RGBGF+$\"#5F)F+-Ffp6$7$7$$\"\"\"F+F*FjnFip-Ffp6$7$F LFgoFip-Ffp6$7$FbqFLFip-Ffp6$7$F?FjnFip-Ffp6$7$F?FgoFip-Ffp6$7$FbqFdpF ip-Ffp6$7$F1FdpFip-F/6#Fbq-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Cu rve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "C urve 11" 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