所有課件-第七次課程材料

第六講:第六講:數(shù)學(xué)模型和算法的應(yīng)用 實(shí)中 力201773:圖論圖論 :哥尼斯堡七橋問(wèn)圖論圖論 :哥尼斯堡七橋問(wèn)Ae5Ae5DBC 7 1 21 24 3研究對(duì)象,圖論中的圖通常某表:近幾年MCM中用到圖論和網(wǎng)絡(luò)的特等獎(jiǎng)統(tǒng)2011MCM-數(shù)42012MCM-72013ICM-52014MCM-12014ICM-62015ICM-6

頂點(diǎn)集邊集頂點(diǎn)集邊集GGφGφG:E(G)?→環(huán)ubayvghecfxwdV(G)ubayvghecfxwdV(G)={u,v,w,x,φG(e)=vx=ubayvghecfxwdb為環(huán)；a為連桿；d，f為重ububayvghecfxwdubayvghecfxwd頂點(diǎn)集弧集G頂點(diǎn)集弧集GubayvgheubayvghecfxwdV(G)={u,v,w,x,φG(a)=(u,v)=GφG:A(a)?→evevvGG?V(HV(GE(HE(G)，則稱HG的子圖 126767543543d?1(x)=d+1(x)=d?1(x)=d+1(x)=路路圈樹(shù)ubaygubaygvhecfxwabcdefgh uvwxyu1200001 u2101v1010100 v1011w0011010 w0102x0001111 x1120y0000000 y0001dGMA關(guān)聯(lián)矩陣Mmve)，mve012表示邊e與頂點(diǎn)v關(guān)鄰接矩陣Aauv)，auv表示是否存在從頂點(diǎn)uv的弧uayfvuayfvgdbxeabcdefgu10000?v??0100w01?010x001??1y000000uvwxyu0001v1010w0001x0110y0000cwDMA關(guān)聯(lián)矩陣M=(mva)，mva1?10}分表a關(guān)聯(lián)的關(guān)系（尾、頭、其它鄰接矩陣Aauv)，auv表示是否存在從頂點(diǎn)uv的弧ubayvubayvghecfxwdGvdG(v)=d?(vd+(v)CCD(v)=CCCC(v)=1∑CB(v)CE(v)=xv= xu= 1 1 p找無(wú)(有向圖的(強(qiáng)/弱連通求從一頂點(diǎn)出發(fā),

a32c6a32c6b315e1d42f000000200000360000050000031100000240(2,2(3,3(3,6(4,5?(5,3(5,1(5,1(6,2(6,401[a,b,c,d,e,f]=W=[dist,path,pred]=graphshortestpath(W,a,02abcdef03w=023000%206530%360010%050012%031104%00024%01n=10;%%給ArBetty,Jane標(biāo)號(hào)為1,2,Andre=1;Betty=2;Carol=3;Dave=4; =Fanny=6;Garth=7;Hale=8;Ike=9;Jane%根據(jù)圖構(gòu)造鄰接矩陣.06A=zeros(n);07A(Andre,[Betty,Carol,Dave,Fanny])=1;08A(Betty,[Andre,Dave,Ed,Garth])=1;09A(Carol,[Andre,Dave,Fanny])=1;A(Dave,[Andre,Betty, Ed,Fanny,Garth])=A(Ed,[Betty,Dave,Garth])=A(Fanny,[Andre,Carol,Dave,Garth,Hale])=A(Garth,[Betty, Ed,Fanny,Hale])=A(Hale,[Fanny,Garth,Ike])=A(Ike,[Hale,Jane])=A(Jane,[Ike])=Cd=degrees(A)'/(n-1)%計(jì)算點(diǎn)度中心度并標(biāo)準(zhǔn)化Cc=closeness(A)*(n-1)%計(jì)算接近中心度并標(biāo)準(zhǔn)化

HaleJane55 6313407W=08[dist,path,pred]=graphshortestpath(W,1,1101w=023000%206530%360010%050012%031104%000240];%G(VW)w(vivj)vsvt間存在一∑w(μ)= w(vi,554155G(VE)w(vivj)TE且為無(wú)循環(huán)圖,使權(quán)T的總權(quán)最小∑w(T)= w(vi,4053350535502433201334101w01w=[04inf5infW=[ST,pred]=G(VW)G(VW)邊權(quán)為w(vivj)GC,的總權(quán)最∑w(C)= w(vi,01R=02dist=zeros(n);03fori=1:nforj=ist(i,j)=istacelati),loi,lat,lo(j,;6 d[order,totdist]=QIKRPMJOCHGDE 所在地(鎮(zhèn))AB···12···分三組（路）graphallshortestpaths函數(shù)求得明確目標(biāo)：將G分成三個(gè)子圖G(V),G(V)子頂點(diǎn)集中都包含頂點(diǎn)O:O∈Vi,i=12子頂點(diǎn)集中包V中所有頂點(diǎn):Vi最小Hamilton回路長(zhǎng)度總和最小化mi