Igraphic Theory

I-theory yegrafu ingenye yezigatshana zeemathematika, into ebonakalayo ebonakalayo yindlela yejometri ekufundeni izinto. Umsunguli walo uthathwa ngokuba yi- mathematikistanist L. Euler.

Ukusetyenziswa kweengcamango zegrafu ukuya ekupheleni kwekhulu le-19 kuncitshiswa ekuxazululeni iingxaki ezonwabisayo kwaye azizange zithinte ingqwalasela ebalulekileyo. Ukususela kwinkulungwane ye-20, xa inkolelo yeigrafu iye yaqalisa ukuqeqeshwa kweemathematika ezizimeleyo, ifunyenwe ngokubanzi kwiinkalo zesayensi njenge cybernetics, physics, logistics, program, biology, i-electronics, izithuthi kunye neenkqubo zokunxibelelana.

Iingcamango ezisisiseko zegraphic theory

Igrafu ingundoqo. Kwigama lesiqhelo, umntu unokufumana into enjalo njengethungelwano olufanayo negrafu. Inxalenye yokugqibela iyinani elingenanto ngaphandle kweengongoma, oko kukuthi, izitha, kunye namacandelo, oko kukuthi, imida, zombini iziphelo ezihambelana nenani elinikeziweyo lamaphupha. Igraphic theory ayenzi ingqiqo ecacileyo kwixabiso leemida kunye neendlela. Ngokomzekelo, iidolophu kunye neendlela ezidibanisa kuzo, apho kuqala khona iziqwenga zegrafu, kwaye yesibini - imida. Ubaluleke ngakumbi kwiingcamango zinikezelwa kwii-arcs. Ukuba umgca unesiqendu, ke unalo igama le-arc, ukuba igrafu ineemida ezijoliswe kuyo, ibizwa ngokuba yi-digraph.

Kwisigama sesingqinisiso, ezi ngcamango zilandelayo ziyabonakala:

Igragraph igrafu, yonke imida kunye neendlela zazo eziphakathi kweemilenze kunye nemida.

Igrafu edibanisiweyo yinto elineenkcukacha ezidibanisa kuzo izandi ezimbini ezahlukeneyo.

Igrafu edibeneyo enxulumene nomntu lowo unikwe umsebenzi wakhe wesisindo.

Umthi uyi-graph edibeneyo ngaphandle kwemijikelezo.

I-squelet is a subgraph engumthi.

Xa igrafu ithathwa kwinqwelo, inqaku elithile lisetyenzisiweyo: i-vertex ekhethiweyo ihambelana nephuzu kwindawo elula kakhulu, kwaye ukuba kukho umda phakathi kwee-vertices, kwaye amanqaku afanayo ahlangene nxalenye. Ukuba igrafu ixhomekeke, ezi zigaba zitshintshwa ngokutsha.

Kodwa musa ukuthelekisa umfanekiso wesigrafu kunye naso, oko kukuthi, ngesakhiwo esingabonakaliyo, kuba enye igrafu inokunikezwa ngaphezulu kwesinye imifanekiso eqingqiweyo. Umzobo wendiza unikezelwa ukuze ubone ukuba ziphi iimbini zamehlo ezidibeneyo kunye neendawo ezingekho.

Phakathi kweengxaki zegraphic theory, zikhona:

1. Umsebenzi wenkqutshane emfutshane (ukutshintshwa kwezixhobo, ukufakwa kwee-ambulensi kunye nezikhululo zefowuni).
2. Ingxaki yokuhamba kwamanzi (ukulawulwa kwezithuthi kwiinkonzo ezinamandla, ukuhanjiswa komsebenzi, umbutho wamandla).
3. Umsebenzi wokugqoka kunye nokupakishwa (ukubeka kwamanqaku okuthumela).
4. Ukufaka imibala kwiigrafu (ukubeka imemori kwiikhomputha zekhompyutha).
5. Ukunxibelelana kwamanethiwekhi kunye negrafu (ukudala inethiwekhi yonxibelelwano, uhlalutyo lwamanethiwekhi oonxibelelwano).

Okwangoku, akunakwenzeka ukucwangcisa ezininzi zeengxaki ngaphandle kokwazi imfundiso yegrafu. Oku kwenza kube lula kwaye kulula ukusebenza kunye nekhompyutha.

Iprogram isebenzisa ezininzi izakhiwo kunye neendlela zokusombulula iingxaki, kunye enye yazo i-theory. Ukubaluleka kwalo kubunzima ukugqithisa. Igraphic theory kwiprogram yenza kube lula ukufumana ulwazi, ukwandisa iinkqubo, ukuguqula nokusabalalisa idatha. Ngombulelo kwi-algorithms ye-theory, kuya kuba nako ukuyisebenzisa nokuvavanya ekusebenziseni ukuxazulula iingxaki ezithile, ukuguqula i-algorithm ngaphandle kokunciphisa izinga lokuqinisekiswa kweemathematika kwenguqu yokugqibela yale program.

Ipropati ebalulekileyo yenkqubo yokulawula okanye imodeli yiseti yeentsebenziswano zobuncwane ekuqokelelweni kwezenzo kunye neeyunithi zeedatha. Ezi zakhiwo ziphela kuphela iinxalenye zeenkqubo kunye nolwazi abaguqula ngalo. Ngoko ke, iigrafu ziyisiseko sokwakhiwa komprofeti.