10.1 10.2 ()()10.3

10.1 ?

10.1.1 GG=VEEV

GeEvivj(e)=vivjeeE(e)=evievje

vivj()evivj()evivjvi adj vjvi nadj vj()evivjvivj()e

GGG=VE10.1.2 G=GG

10.1.3 G=()G()G

10.1.4 G=G=W

10.1.5 G=V(vi)(vj)(vivjVvivjE)K|V||V|=nKn

10.1.6 G=vVvvd+(v)vvd-(v)vd(v)d(v)=d+(v)+d-(v)G=vVd(v)v2

G=(G)=max{d(v)|vV}(G)=min{d(v)|vV}G

10.1.1 G=

10.1.2

10.1.7 G=k(v)(vVd(v)=k)GkkG(G)=(G)=k

10.1.8 G1=G2=(1) V2V1E2E1G2G1G2G1(2) V2V1E2E1E2E1G2G1G2G1(3) V2=V1E2E1G2G1G2 G1

10.1.9 G2=G1=uvuvE1uvE2G2V2G2V2GV2G2E2G2E2GE2

10.1.10 G1=G2=G=E2=E-E1G2=G2GG1

10.1.11 G=G1=E1E=G1GG1GG1= G

10.1.12 ()G1=G2=fV2V1vuV1uvE1f(u)f(v)E2(E1E2)G1G2G1G2G1G2G2G1

10.1.13

(1) (2) (3)

(a)3x1(b)3y1

10.1.14(a)(b)

10.1.13

1.1.14

10.2 ()()()()()()

10.2.1 ()G=v0v1vmV()e1e2emEvi-1vieiv0e1v1e2v2emvmv0vm()v0vm()()()v0=vm()()

10.2.2 ()()()()()()()()

10.2.3 ()()()()()()()()

10.2.1 vivj()vivj()10.2.2 n(1) ()n-1(2) ()n

10.2.4 vivj()vivjvivjGGG(G)

10.2.5 GGGG=SV-SESG-SS=|v|G-vG=TE-TTVG-TT={e}G-e

G=SVTESSVG+SS={v}G+vG=TETG+TTV

10.2.6 G=SV(G-S)(G)TS(G-T)=(G)SGGS={v}vGGTGT={e}eG

G(G)= {|S||SG}GG(G)=0G(G)=1

(G)= {|T||TG}G(G)=0G(G)=0K1(K1)=0G(G)=1Kn(Kn)=n-1

(H.Whitney)193210.2.3 G(G)(G)(G)10.2.4 Gvuwuwv

10.2.5 Geuwuwe10.2.6 Gee

GGG1G1G

10.2.7 GGGGGGGG

10.2.7 GGGGG1G1G10.2.8

10.2.8 10.2.6{v1,v2,v3}

10.2.9 10.2.10 uv()()()uvd

d0d=0d+dduvd=+uvdd

CPU

Ar1r2Br2r1

Pt={p1p2pm}tQtPttRt={r1r2rn}tGt=trii=12nEpkQtrirj

Rt={r1,r2,r3,r4}Qt={p1,p2,p3,p4}p1r4r1p2r1r2r3p3r2r3p4r3r1r4

Gt=10.2.7tGt10.2.7Gt

10.2.7

10.3 G=()

G=V

10.3.1 G=V={v1v2vn}VnA=(aij)G

ij=12n

GGA(G)

GGHPA(H)=P-1A(G)PV

1

AAGnn

nn

ivii1vij1vjd+(vi)= d-(vj)=

GAAlAlijalijGivijvjl10.3.1 AGAlijalijGvivjl()

vivjvivjGAA2A3AnAr 1vivjvivjAr

10.2.2nn-1n 1rnBn=A+A2+A3++An

10.3.2 G=V={v1v2vn}nP=(pij) 1 vivjPij= 0 PG

{

()()GAPBn=A+A2+A3++AnBn1P

BB={0,1}BC

BCBCBoC(BC)ij=bijcij(BoC)ij= (bikckj)i,j=1,2,,nbijcijBCij

AAoA=A(2)r=2,3,,A(r-1)oA=A(r)ArA(r)Ar vivjrA(r) vivj=1 =0PP=AA(2)A(3)A(n)= A(k)

G=EVVEB

X={x1,x2,,xm}Y={y1,y2,,yn}RXYMR=(rij)1, R rij= 0, i=1,2,,mj=1,2,,n{

RMRF(R)=V|V|=nRR+R+=RR2R3Rk (kn)R1R2A1A2R1R2A1A2R+ =

G=AEE2=EoEvkviEvkvkEvjviE2vjvivj2E2(i,j)1A(2)E2A(k)Ekk=2,3,,nA+=AA(2)A(3)A(n) A+=AA(2)A(3)A(n)=P

EE+A+A+PA(2)A(3)A(n) A(k)A+PWarshallAA+

(1) PA(2) k1(3) i1(4) pik=1j=1,2,,npijpijpkj(5) ii+1in(4)(6) kk+1kn(3)(4)pik=1iki

E1E2A=(aij)B=(bij)E1E2AB(AB)ij=aijbij10.3.2 GviP=(pij)GPT=(pji)PPPTi1vi

VP={p1,p2,,pn}PG=piVPi=1,2,,nEpipjGpipiGA=(aij)A+=( )A+ =1pi

G=W=(wij) w, w[vi,vj]E wij= 0 vivjWG{