
shoonya graph

graph sidhaanthathinte ganithashaasthra mekhalayil, "nall graph" enna padam onnukil poojyakramatthilulla graphineo allengil pakaramaayi, eathenkilum edgeless graphineo soochippikkaam (randaamathethu chilappol "shoonya graph" ennu vilikkunnu).
oordar-seero graph.
poojyakramatthilulla graph, konukalillaattha savisheshamaaya graph aanu (athinaal athinte kramam poojyamaanu). athinoppam arikukalumilla. athinaal poojyatthinte oru saadhaarana graafaanu nall graph. chila rachayithakkal oru graph enna nilayil pariganikkunnathil ninnu ozhivaakkunnu (nirvachanam anusarichu, allengil kooduthal lalithamaayi soukaryathinte kaaryamaayi). saadhuvaaya graphai ulppeduthunnathu upayogapradamaano ennathu sandarbhathe aasrayichirikkunnu. positteev vashath, oru graafinte saadhaarana settu-saidhaanthika nirvachanagalil ninnu swaabhaavikamaayi pinthudarunnu (ithu sheershakavum arikum sajjeekarikkunna kramappeduthiya jodiyaanu, randum shoonyamaanu), thelivukalil ithu ganithashaasthra inductionte swaabhaavika adisthaana kesai varthikkunnu, athupole, aavarthichulla nirvachikkapetta dattaa gadanakalil aavarthanathinulla adisthaana cases nirvachikkaan upayogapradamaanu (shoonyamallaatha eathenkilum bainari treal nashtamaaya arikukalude kuttiyayi nall treay kanakkaakkunnathiloode, shoonyamallaatha oro bainari treak "krithyamaayi" rund kuttikal undu). negatteevu vashath, oru graph ulppede, graph propertykalkkaayi nannayi nirvachikkapetta niravadhi soothravaakyangalil athinte ozhivaakkalukal ulppeduthendathundu (udaaharanathinu, onnukil, "oru graafinte shakthamayi bandhippichirikkunna ellah gadakangalum ennunnathu" "oru graafinte" noonn-nall "aayi shakthamayi bandhippichirikkunna ellah gadakangalum ennunnathu" aayi maarunnu, allengil bandhippicha graafukalude nirvachanam ulppeduthaathirikkaan parishkkarikkendathundu). atharam ozhivaakkalukalude aavasyakatha ozhivakkaan, sandarbham mattuvidhathil nirddeshikkunnillengil, "graph" enna padam "kuranjathu oru sheershakamulla graph" ennaanu soochippikkunnathennu saahithyathil palappozhum anumaanikkappedunnu.
kattagari sidhaanthathil, "graafukalude vibhaagam" ennathinte chila nirvachanangal anusarichu, kramam-poojya graph, vibhaagathile prarambha vasthuvaan. 
 graph propertykalil bhooribhaagavum (shoonyamaayi) niravettunnu (oru sheershakavum arikukalumillaatha graph). chila udaaharanagal pole, valippam poojyamaanu, ithu athinte pooraka graph, oru vanam, oru planner graph ennivaykku thulyamaanu. ithu dishaabodhamillaathatho, nirddeshikkappettatho allengil randum koodiyatho aayi kanakkakkaam; nirddeshikkappettathaayi kanakkaakkumbol, ithu oru directed asyclic graafaanu. ithu oru samboornna graph oru edgeless graph aanu. ennirunnaalum, sandarbham anuvadikkunnundo ennathine aashrayich eee graph propertykalude oronninteyum nirvachanangal vyathyaasappedum.
edgeless graph.
oro swaabhaavika samkhyaykkum, kramatthinte edgeless graph (allengil shoonya graph) konukalum poojya arikukalumulla graafaanu. poojyakramatthilulla graph anuvadaneeyamallaatha sandarbhangalil oru edgeless graph idaykkide nall graph ennu vilikkappedunnu.
ithu 0-regular graafaanu. - vertex edgeless graph poornna graafinte poorakamaanenna vasthuthayil ninnaan notteshan undaakunnath.