
insidence matricks

ganita saastramlo, insidence matricks anedi rendu taragatula vastuvula madhya sambandhaanni choopinche taarkika matricks, dheenini saadhaaranamgaa insidence relation anie pilustaaru. modati taragati "x" mariyu rendavadi "y" ayithe, maatrikalo "x" yokka prati muulakaaniki oka varusa mariyu "y" yokka prati muulakaaniki oka niluvu varusa untundi. x" mariyu "y" anae panktulu anusandhaaninchabadinatlayite "x" mariyu "y" anae niluvu varusalooni namodu 1 avutundi (eee sandarbhamlo "sanghatana" anie pilustaaru) mariyu kakapothe 0 avutundi. vaividhyaalu unnaayi; krinda chudandi.
graph siddhaantam.
insidence matricks anedi graph siddhaantamlo oka saadhaarana graph praatinidhyam. idhi vertex-vertex jatala sambandhaanni encode chese prakkane unna maatrikaku bhinnamgaa untundi.
daari mallinchani mariyu nirdesinchina graphlu.
graph siddhaantamlo daari mallinchani graph rendu rakaala insidence maatrikalanu kaligi untundih ann oriented mariyu oriented.
daari mallinchani graph yokka "ann oriented insidence matricks" (ledhaa kevalam "insidence matricks") anedi oka suutram _ 1 matricks "bii", ikkada "enn" mariyu "emm" anevi varusaga sheershaalu mariyu anchula sankhyalu, antey
udaaharanaku, kudi vaipuna chuupina dhisha laeni graph yokka insidence matricks 4 varusalatho (naalugu sheershaalaku anugunamgaa, 1-4) mariyu 4 niluvu varusalatho (naalugu anchulaku anugunamgaa, suutram _ 3) kuudina matricks
manam insidence matricksnu pariseelisthe, prati kaalam yokka mottam 2kii samanamga untundani manam chustamu. endukante prati anchu prati chivarana anusandhaaninchabadina sheershaanni kaligi untundi.
nirdesinchina graph yokka "insidence matricks" anedi suutram _ 1 matricks "b", ikkada "n" mariyu "m" anevi varusaga sheershaalu mariyu anchula sankhya, antey
dhisha laeni graph yokka "oriented insidence matricks" anedi insidence matricks, directed graphla ardhamlo, graph yokka edainaa orientation. antey, anchu "e" yokka niluvu varusalo, "e" yokka oka sheershaaniki anugunamgaa varusalo okati mariyu "e" yokka itara sheershaaniki anugunamgaa varusalo okati −1 untundi, mariyu anni itara varusalaku 0 untundi. oriented insidence matricks edainaa niluvu varusala yokka niraakarana varaku pratyekamainadi, endukante niluvu varusa yokka entreelanu tiraskarinchadam anedi anchu yokka dhoranini tippadaaniki anugunamgaa untundi.
graph "g" yokka ann oriented insidence matricks krindi siddhaantam dwara daani line graph "l" ("g") yokka prakkane unna matricks kuu sambandhinchinadih
ikkada "a" ("l" ("g")) anedi "g" yokka line graph yokka prakkane unna matricks, "b" ("g") anedi insidence matricks, mariyu "i" m "anedi dimension" m "yokka identity matricks.
vivikta laplasian (ledhaa kirchaff matricks) suutram dwara oriented insidence matricks "bii" ("zii") nundi pondabadutundi.
graph yokka samagra chakra sthalam daani aadhaarita insidence matricks yokka shoonya sthalaaniki samanamga untundi, dheenini puurnaamkaalu ledhaa vaastava ledhaa sanklishta sankhyalapai maatrukagaa chuustaaru. binary saikil space anedi daani oriented ledhaa ann oriented insidence matricks yokka shoonya sthalam, dheenini rendu-muulakaala kshetrampai oka matrixga chuustaaru.
santakam chesina mariyu rendu disalalo unna graphlu.
santakam chesina graph yokka insidence matricks anedi oriented insidence matricks yokka saadhaaraneekarana. idhi icchina santakam chesina graphnu orient chese edainaa dvidisaatmaka graph yokka insidence matricks. oka saanukuula anchu yokka niluvu varusalo oka mugimpu binduvuku anugunamgaa oka 1 mariyu itara mugimpu binduvuku anugunamgaa varusalo a − 1 untundi, saadhaarana (santakam cheyani) graphloni anchu vale. pratikuula anchu yokka niluvu varusa rendu varusalo a1 ledhaa a−1 kaligi untundi. line graph mariyu kirchaff maatrika lakshanaalu santakam chesina graphlaku saadhaaraneekarinchabadataayi.
bahulalekhanaalu.
insidence matricks yokka nirvachanalu looplu mariyu bahula anchulatho unna graphlaku vartistaayi. oka loopku anugunamgaa unde oriented insidence matricks yokka kaalam sunna, graph santakam cheyabadi, loop pratikuulamgaa unte tappa; appudu kaalam daani incident vertex varusalo ±2 minaha mottam sunna avutundi.
baruvunna graphlu.
oka baruvaina graphnu 1 sthaanamlo anchu baruvunu upayoginchi suuchimchavachchu. udaaharanaku, kudi vaipuna unna graph yokka insidence matricks
hyper graphlu.
saadhaarana graphla anchulu rendu sheershaalanu matrame kaligi untaayi (prati chivara okati), graphla kosam insidence matricks yokka kaalamlo rendu sunna kaani entreelu matrame untaayi. dheeniki viruddhamgaa, hypergraph oka anchuku ketaayinchina bahula sheershaalanu kaligi undavacchu; anduvalla, pratikuulam kaani puurnaamkaala yokka saadhaarana maatruka hypergraphnu vivaristundi.
sanghatana nirmaanaalu.
insidence structure "c" yokka "insidence matricks" anedi oka matricks "b" (ledhaa daani transpose), ikkada "p" mariyu "q" anevi varusaga "paayintlu" mariyu "linelu" sankhyalu, antey point "p" i mariyu line "l" "j" incident ayithe mariyu 0 lekapothe. eee sandarbhamlo, insidence matricks kooda nirmaanam yokka levi graph yokka biogessancy matricks. prati levi graphku hypergraph unnanduna, mariyu "dheeniki viruddhamgaa", insidence structure yokka insidence matricks hypergraphnu vivaristundi.
parimita jyaamitulu.
oka mukhyamaina udaaharana parimita jyaamiti. udaaharanaku, parimita samatalamlo, "x" anedi paayintla samiti mariyu "y" anedi rekhala samiti. adhika parimaanam yokka parimita jyaamitiloo, "x" anedi paayintla samiti kaavacchu mariyu "y" anedi mottam sthalam yokka parimaanam (hyper plains) kante oka takkuva parimaanam yokka upasthaanaala samiti kaavacchu; ledhaa, marinta saadhaaranamgaa, "x" anedi oka parimaanam "d" mariyu "y" yokka anni upasthaanaala samiti kaavacchu, maroka parimaanam "e" yokka anni upasthaanaala samiti, insidence containmentga nirvachinchabadindi.
polytopes.
idhe paddhatiloo, polytoploni kolatalu okadaanitoe bhinnamgaa unde kanaala madhya sambandhaanni insidence matricks dwara suuchimchavachchu.
designlanu nirodhinchandi.
maroka udaaharana block design. ikkada "x" anedi "paayintla" parimita samiti mariyu "y" anedi "x" yokka upasamitula taragati, dheenini "blocks" anie pilustaaru, idhi design rakampai aadharapadi unde niyamaalaku lobadi untundi. block designla siddhaantamlo insidence matricks oka mukhyamaina sadhanam. udaaharanaku, idhi matsyakaarula asamaanatanu niroopinchadaaniki upayoginchavacchu, idhi samatulya asampoorna 2-designla (bibbs) yokka praathamika siddhaantam, blackla sankhya kaneesam paayintla sankhya anie. blacklanu setla vyavasthagaa pariganinchi, insidence matricks yokka saasvatamainadi vibhina pratinidhula (sdrs) vyavasthala sankhya.

