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1、Chapter9: Undirectedgraphs andnetworksThomasZhou总体浏览9.1KickoffwithCAS9.2Basicconceptsofanetwork9.3PlanargraphsandEuler’sformula9.4Walks,trails,paths,cyclesandcircuits9.5Treesandtheirapplications9.6Review单词Vertex----顶点Edge---边Isolatedvertex---孤立顶点Loop----回路Paralleledges----平
2、行边Multipleedges----多重边Simpleconnection----简单连接Node---节点，结点，网点单词Degree---度Isomorphic---同形Diagonallysymmetric---对角对称例1：Countthenumberofverticesandedgesinthenetworkshown.例2Determinethedegreeofeachvertexinthefigureshown.例3Labeltheverticesandedgesforthefigureshown,Therearesevera
3、lpointstonoteaboutthisrepresentation:1.thereisno‘3’inthelistofedges(E).Thisimpliesitisanisolatedvertex.2.thenumberofpairsinE{(1,4),(1,2),...}=8whichmustbethesameasthenumberofedges3.thenumberoftimesavertexappearsanywhereinsideEequalsthedegreeofthevertex.Forexample,thedigit4a
4、ppears5times,sothedegreeofvertex4=5.4.fromthisrepresentationofVandEwecanconstruct(orreconstruct)theoriginalgraph.例4Constructagraph(network)fromthefollowinglistofverticesandedges.V={A,B,C,D,E}E={(A,B),(A,C),(A,D),(B,C),(B,D),(B,D),(C,E),(D,E),(E,E)}例5Representthenetworkshown
5、(fromWorkedexample4)asamatrix.矩阵方法数度的时候，要将对角线上的数加*2，因为是回路是二度的。作业：9.2T1,3,5,7,9,10,12,13,16例题Constructanetworkfromthefollowinglistofverticesandedges.thencalculatethedegreeofeachvertexaV={1,2,3,4}E={(1,2),(1,4),(2,3),(3,4)}例题Constructanetworkfromthefollowinglistofverticesande
6、dges.thencalculatethedegreeofeachvertexbV={A,B,C,D,E}E={(A,B),(A,C),(A,C),(B,B),(B,C),(B,D),(C,D)}例题Consideranetworkof4vertices,whereeachvertexisconnectedtoeachoftheother3verticeswithasingleedge(noloops,isolatedverticesorparalleledges).aListtheverticesandedges.bConstructadi
7、agramofthenetwork.cListthedegreeofeachvertex例题Constructanetworkrepresentingthefollowingfamilytree.Useasinglenodetorepresenteachmarriedcouple.AllanandBettyhad3children:Charles,DorisandEarl.CharlesmarriedFrancesandhad2children,GeorgeandHarriet.DorismarriedIanandhad1child,John
8、.EarlmarriedKarenandhad3children,Louise,MaryandNeil.例题Representthefollowingnetwork
