
abhivinyas (graph siddhant)

graph siddhant mein, ack dishaheen graph kaa abhivinyas pratyek kinare kii disha kaa ack kaary haye, joe praarambhik graph koo ack nirdeshit graph mein badal detaa haye.
unmukh graph.
ack nirdeshit graph koo ack unmukh graph kahaa jaataa haye yadi isake sheershon key jode mein seey koee bhee dou samamit kinaaron seey naheen judaa hotaa haye. nirdeshit graphon mein, unmukh graph way hain jinamen koee 2-chakr naheen hain (joe graph key teeron mein seey ack hoe sakata haye).
ack pratiyogita ack poorna graph kaa abhivinyas haye. polytery ack dishaheen pedh kaa abhivinyas haye. sumner kaa anuman bataata haye kii sheershon vaale pratyek tournament mein sheershon vaale pratyek polytery hotey hain.
sheershon (key liye) key saath gair-samroop unmukh graph kii sankhya haye
tournament poorna nirdeshit graph (graph jisamen pratyek jodee key alag-alag sheershon key beach ack yaa donon dishaaon mein ack nirdeshit kinara hotaa haye) key saath ack-seey-ack patrachar mein hotey hain. ack poorna nirdeshit graph koo pratyek 2-chakr koo hataakar ack unmukh graph mein parivartit kiya jaa sakata haye, aur isake vipareet ack unmukh graph koo pratyek jodee sheershon key beach ack 2-chakr jodkar ack poorna nirdeshit graph mein parivartit kiya jaa sakata haye joe ack kinare key antim bindu naheen hain; yeye patrachar dwi-uddeshya hain. isaliye, sankhyaon kaa ack hii anukram poorna degraph key liye graph ganana samasya koo bhee hull kartaa haye. iss anukram mein sankhyaon key liye ack spasht lekin jatil sootra haye.
seemit abhivinyas.
ack majboot abhivinyas ack abhivinyas haye joe ack dridhata seey judey graph mein parinam detaa haye. nikatata seey sambandhit poori tarah seey chakreeya abhivinyas abhivinyas hain jinamen pratyek kinara cumm seey cumm ack saral chakr seey sambandhit haye. ack dishaheen graph kaa abhivinyas poori tarah seey chakreeya hotaa haye yadi aur kewal tabhi jaba yeh pratyek judey hue ghatak kaa ack majboot abhivinyas hoe. robbins kii pramey bataati haye kii ack graph kaa ack majboot abhivinyas hotaa haye yadi aur kewal tabhi jaba yeh 2-kinare seey judaa hoe; disconnect kiye gaye graph mein poori tarah seey chakreeya abhivinyas hoe sakate hain, lekin kewal tabhi jaba unake paas koee pull naa hoe.
ack chakreeya abhivinyas ack abhivinyas haye jiska parinam ack nirdeshit chakreeya graph mein hotaa haye. pratyek graph mein ack chakreeya abhivinyas hotaa haye; sabhi chakreeya abhivinyason koo ack anukram mein sheershon koo rakhkar praapt kiya jaa sakata haye, aur phir pratyek kinare koo anukram mein apane antim binduon key pahale seey baad key antim bindu taka nirdeshit kiya jaa sakata haye. gallai-haise-roy-vitevar pramey bataata haye kii ack graph mein ack chakreeya abhivinyas hotaa haye jisamen sabse lambe maarg kaa adhikansh sheershon parr hotaa haye yadi aur kewal tabhi jaba ise adhikansh rangon key saath rangeen kiya jaa sakata haye. chakreeya abhivinyas aur poori tarah seey chakreeya abhivinyas samtaliya dwaitata dwara ack dusare seey sambandhit hain. ekal srot aur ekal sink key saath ack chakreeya abhivinyas koo dwidhruvi abhivinyas kahaa jaataa haye.
ack sankramansheel abhivinyas ack abhivinyas haye kii parinami nirdeshit graph iska apana sankramansheel samaapan haye. sankramansheel abhivinyas vaale graph koo tulanaatmak graph kahaa jaataa haye; jaba bhee way aanshik crum mein tulaniya hotey hain tou unhein dou tatvon koo sanlagn karke aanshik roop seey krambaddh sett seey paribhaashit kiya jaa sakata haye. ack sankramansheel abhivinyas, yadi ack maujood haye, tou raikhik samay mein paaya jaa sakata haye. haalaanki, yeh pareekshan karane key liye kii kyaa parinami abhivinyas (yaa koee diyaa gayaa abhivinyas) vaastav mein sankramansheel haye, adhik samay kii aavashyakta hoti haye, kyonki yeh jatilata mein matricks gunan key barabar haye.
ack dishaheen graph kaa ack ularian abhivinyas ack abhivinyas haye jisamen pratyek sheersh mein degree aur degree key baahar samaan hotaa haye. grid graph key ularian abhivinyas burf-prakaar model key siddhant mein saankhyikiya yantriki mein utpann hotey hain.
ack piphaphian abhivinyas mein yeh guna hotaa haye kii graph mein kuchh summ-lambai vaale chakron mein chakr key chaaron or dou dishaaon mein seey pratyek mein unmukh kinaaron kii ack visham sankhya hoti haye. way hamesha samtal graph key liye maujood hotey hain, lekin kuchh anya graph key liye naheen. way sahee milan kii ginati key liye aff. key. tii. algorithm mein upayog kiye jaate hain.

