Nazariyai grafho

Nazariyai grafho yak fasli matematikaro guyand, ki obekthoyashro ba tariqi geometri meomuzad. Mafhumi asosii in nazariya graf meboshad. Graf tavassuti majmui qullaho (nuqtaho) va majmui teuaho (bandho)-e, ki baze az jufthoi (yo haman) qullahoro mepayvandand, muayyan karda meshavad. Jufthoi qullaho ba hamdigar bo yakchand tegakho payvast shuda metavonand. Masalan, majmui shahrhoi Tojikiston (qullahoi graf) va rohhoe, ki in shahr- horo mepayvandand (tegahoi graf); elementhoi skhemai elektri (qulla) va simhoi onhoro payvastkunanda (tegaho). Vazifai asosii Nazariyai grafhoro intikhob namudann tegahoi optimali (masalan, rohhoi kutohtarin) tashkil medihad. Agar dar tegaho samt va yo tartibi az qullaho guzashtan muay­yan shuda boshad, graf samtdor nomi­da meshavad.

Yake az korhoi avvalin dar sohai Nazariyai grafho tadqiqoti L. Eyler doir ba halli masala va misolhoi matematikai shavqovar ast. Avvalin natijahoi daqiq doir ba Nazariyai grafho dar nimai yakumi asri 20 dar zimni tartib dodani zanjirhoi alektri, hisob kardani moddahoi khimiyavvi navi payvasthoi molekulaviashon guno- gun ba vujud omadand. Solhoi 50 asri 20 vobasta ba inkishofi kibernetika va tekhnikai hisobbarori Nazariyai grafho bo surat taraqqi namud va bo materi­alu usulhoi nav boy gardid. Nazariyai grafho dar nazariyai programmasozi, dar bunyodi kompyuterho, omuzishi pro­sesshoi fiziki, khimiyavi va tekhno­logi, halli masalahoi baplangiry, dar zabonshinosi va tadqiqoti sotsi­ologi istifoda burda meshavad. Nazariyai grafho bo gopologiya, algebra, tahlili kom- binatori, nazariyai adadho va digar sohahoi matematika robitai mustahkam dorad.

Ad.: B e r j K., Teoriya grafov eyo pri­meneniya. per. s frants.. M., 1962; Ore O., Grafi i ikh primenenie, per. s angl., M„ 1965; Basaker R., S a a t i T., Konechnie grafi i seti, per. s angl., M.,