This Maple 10 worksheet demonstrates some of the functionality and design of the new GraphTheory package being developed by people at SFU. It was created by Mahdad Khatarinejad and presented by Mahdad at the Maple company premises on Wednesday July 20th, 2005. The content were subsequently adjusted somewhat by Mike so that the reader can infer what the purpose of some of the examples are. This version of the worksheet has been updated by Michael Monagan in June 2006 to work with GTv24 - version 1.24 of the GraphTheory package. This version of the worksheet has been updated by Michael Monagan in August 2006 to work with GTv26 - version 1.26 of the GraphTheory package

A Graph Theory Package for Maple Mahdad Khatirinejad Department of Mathematics, SFU Joint work with: Jeff Farr Sara Khodadad Michael Monagan Waterloo, 20 July, 2005

restart; currentdir("/home/mmonagan/GraphTheory/GTv26");

UUEvaG9tZS9tbW9uYWdhbi9HcmFwaFRoZW9yeS9HVHYyNjYi

read "GTv26.txt";

with(GraphTheory);

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

with(SpecialGraphs);

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

with(RandomGraphs);

NylJMkFzc2lnbkVkZ2VXZWlnaHRzRzYiSTVSYW5kb21CaXBhcnRpdGVHcmFwaEdGJEkuUmFuZG9tRGlncmFwaEdGJEksUmFuZG9tR3JhcGhHRiRJLlJhbmRvbU5ldHdvcmtHRiRJMVJhbmRvbVRvdXJuYW1lbnRHRiRJK1JhbmRvbVRyZWVHRiQ=

The networks package over 10 years old designed primarily with applications in networks in mind data structure is too heavy and cumbersome for using in elementary graph theory problems The GraphTheory package (main goals) design primarily for solving problems related to graphs rather than networks keep data structure simple, yet flexible, able to treat graphs of 1000 vertices visualization of graphs is important Some timing comparisons 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: Random graph on 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vertices and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEhRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiVGKy1GIzYkLUkjbW5HRiQ2JVEiM0YnRjIvRjZRJ25vcm1hbEYnLUYsNiZRIm5GJ0YvRjJGNUYrRis= edges n LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiVGKy1GIzYnRistRiM2JUYrLUYjNiMtRiw2JVEiQ0YnRi9GMi1GLDYlUTNvbm5lY3RlZENvbXBvbmVudHNGJ0YvRjJGKy1GIzYnRistSShtZmVuY2VkR0YkNiQtRiM2JUYrLUYjNiUtRiw2JVEiR0YnRi9GMi1JI21vR0YkNjBRMCZBcHBseUZ1bmN0aW9uO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGVy8lKXN0cmV0Y2h5R0ZXLyUqc3ltbWV0cmljR0ZXLyUobGFyZ2VvcEdGVy8lLm1vdmFibGVsaW1pdHNHRlcvJSdhY2NlbnRHRlcvJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRJDBlbUYnLyUncnNwYWNlR0Zjby8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1GRjYkLUYjNiMtRiw2JVEibkYnRi9GMkZTRitGU0YrLUYjNiNGK0YrRitGK0Yr 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 250 0.009 0.05 500 0.009 0.18 1000 0.069 0.201 2000 0.06 0.479 4000 0.139 1.211 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: Random graph on 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vertices and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEhRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiVGKy1GIzYkLUkjbW5HRiQ2JVEiM0YnRjIvRjZRJ25vcm1hbEYnLUYsNiZRIm5GJ0YvRjJGNUYrRis= edges 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 : Half of the vertices of 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 n 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 20 0.0 0.46 40 0.0 12.22 60 0.0 104.12 1000 0.048 ? 2000 0.088 ? 4000 0.219 ? 8000 0.503 ?

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LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDclSSJhRzYiSSJiR0YqSSJjR0YqLUkmQXJyYXlHRiQ2Iy9JJCVpZEdGKiIpQ2MkPSJJMEdSQVBITE4vdGFibGUvMUdGKiIiIQ==

QyQtSSNvcEclKnByb3RlY3RlZEc2I0kjQzNHNiIiIiI=

NihJK3VuZGlyZWN0ZWRHJSpwcm90ZWN0ZWRHSSt1bndlaWdodGVkR0YkNyVJImFHNiJJImJHRihJImNHRigtSSZBcnJheUdGJDYjL0kkJWlkR0YoIilDYyQ9IkkwR1JBUEhMTi90YWJsZS8xR0YoIiIh

GRAPHLN(D, W, V, A, T, EW) D : directed or undirected (type : symbol) W : weighted or unweighted (type : symbol) V : vertex labels (type : list) A : adjacency-list of vertices (type : Array -- of sets of positive integers) T : anything such as vertex positions, edge coloring, ... (type : table) EW: edge weights (type : Matrix) (+ if W=unweighted then EW is not a Matrix and is set to 0) QyQ+SSJIRzYiLUkmR3JhcGhHRiU2JC1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjL0kkJWlkR0YlIilHKnBPIkkpd2VpZ2h0ZWRHRiwiIiI=

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkpd2VpZ2h0ZWRHRiQ3JSIiIiIiIyIiJC1JJkFycmF5R0YkNiMvSSQlaWRHNiIiKVtfcjlJMEdSQVBITE4vdGFibGUvMkdGMS1JJ01hdHJpeEc2JEYkSShfc3lzbGliR0YxNiMvRjAiKUcqcE8i

QyQtSSNvcEclKnByb3RlY3RlZEc2I0kiSEc2IiIiIg==

NihJK3VuZGlyZWN0ZWRHJSpwcm90ZWN0ZWRHSSl3ZWlnaHRlZEdGJDclIiIiIiIjIiIkLUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIpW19yOUkwR1JBUEhMTi90YWJsZS8yR0YvLUknTWF0cml4RzYkRiRJKF9zeXNsaWJHRi82Iy9GLiIpRypwTyI=

QyQtSSZFZGdlc0c2IjYjSSJIR0YlIiIi

PCU8JCIiIiIiIzwkRiUiIiQ8JEYkRic=

DrawGraph(H);

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

QyQ+SSJQRzYiLUkuUGV0ZXJzZW5HcmFwaEdGJUYlIiIi

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDcsIiIiIiIjIiIkIiIlIiImIiInIiIoIiIpIiIqIiM1LUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIoIz5XJylJMEdSQVBITE4vdGFibGUvNUdGOCIiIQ==

QyQtSSNvcEclKnByb3RlY3RlZEc2I0kiUEc2IiIiIg==

NihJK3VuZGlyZWN0ZWRHJSpwcm90ZWN0ZWRHSSt1bndlaWdodGVkR0YkNywiIiIiIiMiIiQiIiUiIiYiIiciIigiIikiIioiIzUtSSZBcnJheUdGJDYjL0kkJWlkRzYiIigjPlcnKUkwR1JBUEhMTi90YWJsZS81R0Y2IiIh

The table is used to store vertex positions, which have been precomputed, so that when drawn, the Petersen graph displays in (one of) the standard drawings. DrawGraph(P);

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Constructing graphs .... C1 := CompleteGraph([1,2,3,4]);

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDcmIiIiIiIjIiIkIiIlLUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIpKUd5MCJJMEdSQVBITE4vdGFibGUvN0dGMiIiIQ==

C2 := CompleteGraph([5,6,7,8]);

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDcmIiImIiInIiIoIiIpLUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIpOyMzMCJJMUdSQVBITE4vdGFibGUvMTBHRjIiIiE=

C := DisjointUnion(C1,C2);

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDcqIiIiIiIjIiIkIiIlIiImIiInIiIoIiIpLUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIpVyJcOyJJMUdSQVBITE4vdGFibGUvMTJHRjYiIiE=

AddEdge(C, {4,5});

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDcqIiIiIiIjIiIkIiIlIiImIiInIiIoIiIpLUkmQXJyYXlHRiQ2Iy9JJCVpZEc2IiIpVyJcOyJJMUdSQVBITE4vdGFibGUvMTJHRjYiIiE=

DrawGraph(C);

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IsBiconnected(C);

SSZmYWxzZUclKnByb3RlY3RlZEc=

BiconnectedComponents(C);

NyU3JCIiJSIiJjcmIiIiIiIjIiIkRiQ3JkYlIiInIiIoIiIp

Problem: Find a Spanning Tree and the Spanning Polynomial of a given connected graph G := RandomGraph(12,.3): while ChromaticNumber(G)=1 or not(IsConnected(G)) do G := RandomGraph(12,.3): od: DrawGraph(SpanningTree(G));

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

f := SpanningPolynomial(G, p);

LDAqJEkicEc2IiIjNiIlLDoqJEYkIiM3ISUmNCgqJEYkIiM4IiZsVCIqJEYkIiM5ISZsXyIqJEYkIiM6IiVgJCoqJEYkIiM7ISUnMyQqJEYkIiM8IiRHJQ==

eval(f, p=.5);

JCIrLTBXd1IhIzY=

Problem: Find the maximum clique (maximum independent set) in a graph. Algorithm: Backtracking (Branch & Bound) MaximumIndependentSet(G);

NygiIiMiIiQiIiYiIiciIigiIzc=

MaximumClique(G);

NyUiIiMiIikiIio=

ChromaticNumber(G,bound);

OyIiJCIiJQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiMtRiw2J1EibkYnLyUlYm9sZEdGMUYvL0YzUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GLDYnRi5GOkYvRjxGPg== : Number of vertices of G \316\261 : Independence number of G (maximum size of an independent set) \317\207 : Chromatic number of G LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiMtRiw2J1EiZ0YnLyUlYm9sZEdGMUYvL0YzUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GLDYnRi5GOkYvRjxGPg== : Number of colors in a greedy coloring of G Then LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiVGKy1JJm1mcmFjR0YkNigtRiM2Iy1GLDYlUSJuRidGL0YyLUYjNiRGKy1GLDYlUSgmYWxwaGE7RicvRjBRJmZhbHNlRicvRjNRJ25vcm1hbEYnLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZNLyUpYmV2ZWxsZWRHRkVGK0Yr \342\251\275 \317\207 \342\251\275 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Problem: Proper (circular) coloring of vertices or edges of a graph Algorithm: Backtracking ChromaticNumber(G);

IiIk

Pet := PetersenGraph(): DrawGraph(Pet);

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EdgeChromaticNumber(Pet, 'ColorClasses');

IiIl

ColorClasses;

NyY8JjwkIiIiIiIjPCQiIioiIzU8JCIiKCIiKTwkIiIkIiIlPCY8JEYvRik8JEYlIiImPCRGJkYoPCQiIidGKzwmPCRGJUY2PCRGLkYrPCRGL0YzPCRGLEYoPCU8JEYzRiw8JEY2Rik8JEYmRi4=

HighlightEdges(Pet,ColorClasses[1],red); HighlightEdges(Pet,ColorClasses[2],green); HighlightEdges(Pet,ColorClasses[3],magenta); DrawGraph(Pet);

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Problem: Find the max flow of a given network. Algorithm: Goldberg Push-Preflow Complexity: O(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) V := [s,v1,v2,v3,v4,t];

NyhJInNHNiJJI3YxR0YkSSN2MkdGJEkjdjNHRiRJI3Y0R0YkSSJ0R0Yk

N := Digraph(V, { [[s,v1],16],[[s,v2],13], [[v1,v2],10],[[v2,v1],4], [[v1,v3],12],[[v3,v2],9], [[v2,v4],14],[[v4,v3],7], [[v3,t],20],[[v4,t],4] } ): Vertex_Positions := [[0,0.35],[0.35,0.7],[0.35,0],[0.7,0.7],[0.7,0],[1.05,0.35]]: SetVertexPositions(N,Vertex_Positions); DrawGraph(N);

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MaxFlow(N,s,t);

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Problem: Given a graph, test whether or not the graph is planar. If yes, return the plane embedding. Algorithm: Demoucron, Malgrange, Pertuiset IsPlanar(DeleteEdge(CompleteGraph(5),{1,2}));

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IsPlanar(PetersenGraph());

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IsPlanar(DodecahedronGraph(), 'Faces');

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Faces;

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Problem: Find the minimum cost trip of a salesman that must visit n cities and return home. Algorithm: Backtracking (Branch & Bound) M := LinearAlgebra[RandomMatrix](11,11,generator=rand(100)): for i to 10 do M[i,i] := infinity od: G11:=CompleteGraph(11): s:=time(): TravelingSalesman(G11,M); time()-s;

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Problem: Construct a random graph R, sort it's vertices into decreasing order by degree and plot the adjacency matrix to inspect the density of the graph. R := RandomGraph(100,.5);

LUkoR1JBUEhMTkclKnByb3RlY3RlZEc2KEkrdW5kaXJlY3RlZEdGJEkrdW53ZWlnaHRlZEdGJDdgcSIiIiIiIyIiJCIiJSIiJiIiJyIiKCIiKSIiKiIjNSIjNiIjNyIjOCIjOSIjOiIjOyIjPCIjPSIjPiIjPyIjQCIjQSIjQiIjQyIjRCIjRSIjRiIjRyIjSCIjSSIjSiIjSyIjTCIjTSIjTiIjTyIjUCIjUSIjUiIjUyIjVCIjVSIjViIjVyIjWCIjWSIjWiIjWyIjXCIjXSIjXiIjXyIjYCIjYSIjYiIjYyIjZCIjZSIjZiIjZyIjaCIjaSIjaiIjayIjbCIjbSIjbiIjbyIjcCIjcSIjciIjcyIjdCIjdSIjdiIjdyIjeCIjeSIjeiIjISkiIyIpIiMjKSIjJCkiIyUpIiMmKSIjJykiIygpIiMpKSIjKikiIyEqIiMiKiIjIyoiIyQqIiMlKiIjJioiIycqIiMoKiIjKSoiIyoqIiQrIi1JJkFycmF5R0YkNiMvSSQlaWRHNiIiKSc0ITM6STJHUkFQSExOL3RhYmxlLzE0MkdGXHIiIiE=

sigma := sort([op(Vertices(R))],proc(i,j) evalb(Degree(R,i) > Degree(R,j)) end proc);

N2BxIiNTIiMnKiIjeiIjcCIjbSIjKCoiIyYpIiNjIiNiIiNhIiNbIiNQIiImIiMmKiIjIioiIycpIiN0IiNeIiNSIiNJIiM7IiN1IiNfIiNWIiQrIiIjISkiI2wiI2YiI2UiI10iI1ciI0IiIzgiIigiIyEqIiMpKSIjdyIjcyIjaiIjZyIjWiIjVSIjSyIjSCIjPiIjOiIjJCoiIyQpIiMjKSIjIikiI3IiI3EiI2giI1kiI0wiIzYiIiUiI3YiI24iI1EiIiMiIyoqIiMqKSIjRCIjQyIjPyIiKSIiJyIiJCIiIiIjbyIjWCIjVCIjSiIjRSIjQSIiKiIjKCkiI3giI2kiI08iI04iI0YiIzwiIzkiIzUiI3kiI2AiI00iI0ciIyUpIiNrIiNkIiM9IiMlKiIjNyIjXCIjIyoiIykqIiNA

plots[matrixplot](AdjacencyMatrix(PermuteVertices(R, sigma)), orientation=[0,0], shading=Z, style=PATCHNOGRID);

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The above plot converges to the following plot when n approaches infinity, where n is the number of vertices of the random graph in which every edge is present with probability .5: plot3d(1-max(x,y), x=0..1, y=0..1, orientation=[0,0], shading=Z, style=PATCHNOGRID);

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