padvi (aalekh siddhant)

aalekh siddhantat, aalekhchya shirshakachi degree (kinwa valency) mhanje shirshala shirshala kadachi sankhya; bahulekhanat, eka loop, shirshachya degreemadhye, kathachya done tokansathi 2 yogdan deto. shirobindu sootra _ 1 chee degree sootra _ 2 kinwa sootra _ 3 darshavili jaate. aalekh sootra _ 4 chee kamal degree, sootra _ 5 dware darshavili jaate aanee aalekhchi kiman degree, sootra _ 6 dware darshavili jaate, tee tyachya shirobinduchya degreechi kamal aanee kiman asate. ujavikade darshavilelya bahulekhamadhye kamal padvi 5 aanee kiman padvi 0 aahe.
niyamit aalekhamadhye, pratyek shirobinduchi degree samaan asate aanee mhanoon aapan aalekhatil 'daad' digribaddal bolu shakato. sampoorn aalekh (soochit sootra 7, jethe sootra 8 heey aalekhatil shirobinduchi sankhya aahe) haah eka vishesh prakarcha niyamit aalekh aahe jithe serve shirobindu jastit jaast shakya degree, sootra 9 aahet.
swakshari kelelya aalekhamadhye, shirobindu sootra _ 1 shhee jodalelya sakaratmak kadaa sankhyela sakaratmak deformula _ 11 mhanatat aanee jodalelya nakaratmak kadaa sankhyela nakaratmak deformula _ 11 mhanatat.physa.2014.11.062 "> </ref> <ref naav =" 10.1038/s41598-021-81767-7 "> </ref>
hatmilavani lemma.
degree summ sootra asey sangate qee, aalekh sootra _ 13 dile tarr,
sootra soochit karate qee konatyahi dishaheen aalekhamadhye visham degree asalelya shirobindunchi sankhya summ asate. heey vidhan (tasech degree summ sootra) hastandolan lemma mhanoon olakhale jaate. nantarche naav eka lokpriy ganiteey samasyevarun aale aahe, jeey heey siddha karnyasathi aahe qee lokanchya konatyahi gatamadhye, gatatil itar lokanchya visham sankhyeshi hatmilavani kelelya lokanchi sankhya summ aahe.
padvi kram.
dishaheen aalekhatil ansh kram haah tyachya shirobindu anshancha vadhata naan honara kram aahe; vareel aalekhasathi too (5,3,3,2,1,0) aahe. degree kram haah aalekh aparivartaniy aahe, mhanoon samaroop aalekhancha samaan degree kram asato. tathapi, degree kram, sarvasadharanpane, aalekh advitiyapane olakhat nahee; kahee prakarananmadhye, gair-samaroop aalekh samaan degree kram asato.
ansh anukramachi samasya hii kahee kinwa serve aalekh shodhanyachi samasya aahe, jyamadhye ansh anukram haah sakaratmak purnankancha vadhata naan honara kram aahe. (mage asalelya shunyankade durlaksh kele jaau shakate kaaran aalekhamadhye yogya sankhyene vegale shirobindu jodoon teey kshullakpane lakshat yetat.) eka kram joou kahee aalekh, i chaa degree kram aahe.eae. jyachyasathi degree sequence samasyeche nirakaran asate, tyala graphik kinwa graphikal sequence mhanatat. ansh berries sutracha parinam mhanoon, visham berries asalela konatahi kram, jase qee (3,3,1), aalekhatil ansh kram mhanoon lakshat gheta yet nahee. ulat dekhil kharey aaheh jarr ekhadya anukramachi berries summ asel tarr too bahulekhatil degree kram aahe. asha aalekhchi rachana saral aaheh shirobindu visham anshansah jodya (julani tayar karane) joda aanee urvarit summ-ansh mojani swayam-loopdware bhara.
dilelya padvi kramala sadhya aalekhadvare sakar karata yeil qaa haah prashna adhik aavhanatmak aahe. yaa samasyela aalekh sakshatkar samasya asehi mhanatat aanee ektar erdos-gallai pramey kinwa havel-hakimi algoridamdware sodavali jaau shakate. 
dilelya degree sequences aalekhanchi sankhya shodhane kinwa andaj lavane hii aalekh gananechya kshetrachi samasya aahe.
adhik samanyatah, hypergraphcha degree kram haah tyachya shirobinduchya anshancha vadhanara kram nahee. jarr too kahee sootra _ 15-eksaman hypergraphcha degree kram asel tarr kram sootra _ 15-graphik aahe. visheshtah, sootra _ 17-graphik kram haah graphik aahe. dilela kram sootra 15-graphik aahe qee nahee heey tharvane, sootra 19 sathee bahupadi velet erdos-gallai prameyadvare karata yete parantu serve sootra 20 sathee aine. pii.-purn aahe (dezza ett all.2018).

