
brouver yokka ooha

varnapata graph siddhaantam yokka ganita rangamlo, brouver yokka ooha anedi oka graph yokka laplasian yokka aigen viluvala madhyantara mottaala kosam daani anchula sankhya paramgaa eguva sarihaddulapai andris brouver chesina ooha.
g" anedi saralamaina daari mallinchani graph mariyu "l" ("g") daani laplacian matricks ayithe, daani aigen viluvalu "λ" n "(" l "(" g ")) ≤" λ "n" −1 ("l" ("g")) ≤ anie ooha perkondi... ≤ "λ" 1 ("l" ("g")) santrupti kaligistundi
suutram _ 1
ikkada "m" ("g") anedi "g" yokka anchula sankhya.
kala yokka sthithi.
garishtamgaa 10 sheershaalato unna anni graphlaku eee ooha chellubaatu avtundani ganana dwara brouver dhruveekarinchaaru. t" = 1,2 "," n "-1, mariyu" n "ayithe enni sheershaalaku ayina eee ooha chellubaatu avtundani kooda telusu.
konni rakaala graphlaku, brouver yokka ooha anni "t" kuu mariyu enni sheershaalaku ayina chellubaatu avutundi. mukhyamgaa, idhi chetlaku, mariyu ekachakra mariyu chakrakara graphlaku chellubaatu ayyedi. brouver yokka ooha rendu pedda kutumbaala graphlanu kaligi undani kooda niroopinchabadindi; modati kutumbam graphlu daani prati sheershaalanu ekapaksha sii-cyclic graph yokka sheershaaniki gurtinchadam dwara oka samuuham nundi pondabadataayi, mariyu rendava kutumbam graphlatho koodi untundi, dheenilo garishta puurti dwaipaakshika upagraph yokka anchulanu tolaginchadam anedi oka graphnu istundi, dheeni yokka chinnapati kaani bhagalu sii-cyclic graph. 
yaadruchchika graphla yokka konni shrenulaku, shrungaala sankhya anantam vaipu moggu chooputunnanduna, brouver yokka ooha sambhaavyatatoo okadaaniki moggu chooputundi.