Nyob hauv kev ua lej ntawm daim duab txoj kev xav, ib qho automorphism ntawm daim duab yog ib daim ntawv ntawm symmetry nyob rau hauv uas daim duab yog mapped rau nws tus kheej thaum khaws cia ntawm ntug-vertex txuas. … Qhov ntawd yog, nws yog daim duab isomorphism los ntawm G rau nws tus kheej.
txhais li cas los ntawm automorphism?
Nyob rau hauv lej, ib qho automorphism yog an isomorphism los ntawm cov lej lej rau nws tus kheej. Nws yog, nyob rau hauv ib co kev txiav txim zoo, ib tug symmetry ntawm cov khoom, thiab ib txoj kev ntawm daim ntawv qhia cov khoom rau nws tus kheej thaum khaws cia tag nrho nws cov qauv. Cov txheej txheem ntawm tag nrho cov automorphisms ntawm ib yam khoom tsim ib pab pawg, hu ua pawg automorphism.
Dab tsi yog qhov txawv ntawm automorphism thiab isomorphism?
4 Teb. Los ntawm kev txhais, automorphism yog ib qho isomorphism los ntawm G rau G, thaum an isomorphism tuaj yeem muaj lub hom phiaj sib txawv thiab sau npe. Feem ntau (nyob rau hauv ib pawg), ib qho automorphism txhais tau tias yog isomorphism f:G → G.
Dab tsi ua rau daim duab hloov pauv?
Kev hais lus tsis raug cai, daim duab yog vertex-transitive yog tias txhua qhov vertex muaj tib lub zos ib puag ncig, kom tsis muaj vertex tuaj yeem txawv ntawm lwm yam raws li cov vertices thiab cov npoo ib puag ncig nws.
Puas yog daim duab isomorphic rau nws tus kheej?
Definition. Ib qho automorphism ntawm daim duab yog an isomorphism ntawm daim duab nrog nws tus kheej. Rau vertices u thiab v hauv daim duab yooj yim G, yog tias muaj automorphism ntawm G nrog θ: V (G) → V (G), xws li θ (u)=v cesvertices u thiab v hu ua zoo sib xws. … Cov duab kos tuaj yeem pab qhia qhov sib npaug ntawm daim duab.
