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Package ‘igraph0’ February 15, 2013 Version 0.5.6-2 Date 2013-01-05 Title Network analysis and visualization, old, deprecated package. Author See AUTHORS file. Maintainer Gabor Csardi <[email protected]> Description Network analysis package, old, deprecated version. ’igraph0’ is the old version of the igraph package, kept alive temporarily, for compatibility reasons. In this package,vertices and edges are in- dexed from zero, whereas in ’igraph’,starting from version 0.6, they are in- dexed from one. Please do not use this package for new projects. Depends stats Suggests stats4, rgl, tcltk, RSQLite, digest, graph, Matrix License GPL (>= 2) URL http://igraph.sourceforge.net SystemRequirements gmp, libxml2 Repository CRAN Date/Publication 2013-01-09 19:39:41 NeedsCompilation yes R topics documented: igraph-package . .4 aging.prefatt.game . .6 alpha.centrality . .8 arpack . 10 articulation.points . 13 1 2 R topics documented: as.directed . 14 attributes . 16 barabasi.game . 18 betweenness . 20 biconnected.components . 22 bipartite.projection . 23 bonpow . 24 canonical.permutation . 26 cliques . 28 closeness . 30 clusters . 31 cocitation . 32 cohesive.blocks . 33 communities . 36 components . 37 constraint . 38 conversion . 39 conversion between igraph and graphNEL graphs . 40 decompose.graph . 41 degree . 42 degree.sequence.game . 43 diameter . 45 Drawing graphs . 46 dyad.census . 52 edge.betweenness.community . 53 edge.connectivity . 55 erdos.renyi.game . 57 evcent . 58 fastgreedy.community . 59 forest.fire.game . 61 get.adjlist . 62 get.incidence . 63 girth . 65 graph-isomorphism . 66 graph-motifs . 69 graph-operators . 71 graph.adjacency . 72 graph.automorphisms . 75 graph.bipartite . 76 graph.constructors . 77 graph.coreness . 80 graph.data.frame . 81 graph.de.bruijn . 83 graph.density . 84 graph.famous . 85 graph.formula . 87 graph.full.bipartite . 89 graph.graphdb . 90 R topics documented: 3 graph.incidence . 92 graph.kautz . 93 graph.knn . 94 graph.laplacian . 96 graph.lcf . 97 graph.maxflow . 98 graph.strength . 99 graph.structure . 101 Graphs from adjacency lists . 102 grg.game . 103 growing.random.game . 104 igraph-parameters . 105 igraph.sample . 106 independent.vertex.sets . 107 is.bipartite . 108 is.igraph . 109 is.multiple . 110 is.mutual . 111 iterators . 112 kleinberg . 116 label.propagation.community . 117 layout . 118 layout.drl . 123 layout.merge . 125 layout.star . 126 leading.eigenvector.community . 127 line.graph . 130 minimum.spanning.tree . 131 modularity . 132 neighborhood . 133 page.rank . ..

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Constructions and Enumeration Methods for Cubic Graphs and Trees
Butler University Digital Commons @ Butler University Undergraduate Honors Thesis Collection Undergraduate Scholarship 2013 Constructions and Enumeration Methods for Cubic Graphs and Trees Erica R. Gilliland Butler University Follow this and additional works at: https://digitalcommons.butler.edu/ugtheses Part of the Discrete Mathematics and Combinatorics Commons Recommended Citation Gilliland, Erica R., "Constructions and Enumeration Methods for Cubic Graphs and Trees" (2013). Undergraduate Honors Thesis Collection. 360. https://digitalcommons.butler.edu/ugtheses/360 This Thesis is brought to you for free and open access by the Undergraduate Scholarship at Digital Commons @ Butler University. It has been accepted for inclusion in Undergraduate Honors Thesis Collection by an authorized administrator of Digital Commons @ Butler University. For more information, please contact [email protected]. BUTLER UNIVERSITY HONORS PROGRAM Honors Thesis Certification Please type all information in this section: Applicant Erica R. Gilliland (Name as it is to appear on diploma) Thesis title Constructions and Enumeration Methods for Cubic Graphs and Trees Intended date of commencement May 11, 2013 --~------------------------------ Read, approved, and signed by: tf -;t 'J,- J IJ Thesis adviser(s) D'rt/~ S// CWiV'-~ Date Date t.-t - 2. Z - 2.C?{3 Reader(s) Date Date Certified by Director, Honors Program Date For Honors Program use: Level of Honors conferred: University Departmental MtH1t£W1Ah"LS with ttijutt HoVJQ(5 ik1vrj,,1 r"U)U ",1-111 ttlStl HMbCS V(IIVet>i}\j HtlYlb6 froyrltm I Constructions and Enumeration Methods for Cubic Graphs and Trees Erica R. Gilliland A Thesis Presented to the Department of Mathematics College of Liberal Arts and Sciences and Honors Program of Butler University III Partial Fulfillment of the ncCIuirclllcnts for G rae! ua lion Honors Submitted: April 2:3, 2()1:3 Constructions and Enumeration Methods for Cubic Graphs and Trees Erica It Gilliland Under the supervision of Dr.
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University of Durham Final year project Empire Maps on Surfaces An exploration into colouring empire maps on the sphere and higher genus surfaces Author: Supervisor: Caspar de Haes Dr Vitaliy Kurlin D C 0 7 8 0 E 6 9 5 10 0 0 4 11 B 1' 3' F 3 5' 12 12' 0 7' 0 2 10' 2 A 13 9' A 1 1 8' 11' 0 0 0' 11 6' 4 4' 2' F 12 3 B 0 0 9 6 5 10 C E 0 7 8 0 arXiv:1106.4235v1 [math.GT] 21 Jun 2011 D April 28, 2011 Abstract This report is an introduction to mathematical map colouring and the problems posed by Heawood in his paper of 1890. There will be a brief discussion of the Map Colour Theorem; then we will move towards investigating empire maps in the plane and the recent contri- butions by Wessel. Finally we will conclude with a discussion of all known results for empire maps on higher genus surfaces and prove Heawoods Empire Conjecture in a previously unknown case. Contents 1 Introduction 3 1.1 Overview of the Problem . 3 1.2 History of the Problem . 3 1.3 Chapter Plan . 5 2 Graphs 6 2.1 Terminology and Notation . 6 2.2 Complete Graphs . 8 3 Surfaces 9 3.1 Surfaces and Embeddings . 9 3.2 Euler Characteristic . 10 3.3 Orientability . 11 3.4 Classiﬁcation of surfaces . 11 4 Map Colouring 14 4.1 Maps and Colouring . 14 4.2 Dual Graphs . 15 4.3 Colouring Graphs .
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Package 'Igraph'
Package ‘igraph’ February 28, 2013 Version 0.6.5-1 Date 2013-02-27 Title Network analysis and visualization Author See AUTHORS ﬁle. Maintainer Gabor Csardi <[email protected]> Description Routines for simple graphs and network analysis. igraph can handle large graphs very well and provides functions for generating random and regular graphs, graph visualization,centrality indices and much more. Depends stats Imports Matrix Suggests igraphdata, stats4, rgl, tcltk, graph, Matrix, ape, XML,jpeg, png License GPL (>= 2) URL http://igraph.sourceforge.net SystemRequirements gmp, libxml2 NeedsCompilation yes Repository CRAN Date/Publication 2013-02-28 07:57:40 R topics documented: igraph-package . .5 aging.prefatt.game . .8 alpha.centrality . 10 arpack . 11 articulation.points . 15 as.directed . 16 1 2 R topics documented: as.igraph . 18 assortativity . 19 attributes . 21 autocurve.edges . 23 barabasi.game . 24 betweenness . 26 biconnected.components . 28 bipartite.mapping . 29 bipartite.projection . 31 bonpow . 32 canonical.permutation . 34 centralization . 36 cliques . 39 closeness . 40 clusters . 42 cocitation . 43 cohesive.blocks . 44 Combining attributes . 48 communities . 51 community.to.membership . 55 compare.communities . 56 components . 57 constraint . 58 contract.vertices . 59 conversion . 60 conversion between igraph and graphNEL graphs . 62 convex.hull . 63 decompose.graph . 64 degree . 65 degree.sequence.game . 66 dendPlot . 67 dendPlot.communities . 68 dendPlot.igraphHRG . 70 diameter . 72 dominator.tree . 73 Drawing graphs . 74 dyad.census . 80 eccentricity . 81 edge.betweenness.community . 82 edge.connectivity . 84 erdos.renyi.game . 86 evcent . 87 fastgreedy.community . 89 forest.ﬁre.game . 90 get.adjlist . 92 get.edge.ids . 93 get.incidence . 94 get.stochastic .
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A Practical 4-Coloring Method of Planar Graphs
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