
swatantra sanklishtata

graph yokka swatantra sanklishtata anedi graph yokka swatantra setlanu vivarinche ganita vastuvu. adhikarikamga, i ("g") dwara suchinchabade daari mallinchani graph "g" yokka swatantra sanklishtata, oka nairoopya saralamaina sanklishtata (antey, upasamitulanu teesukune operation kinda moosiveyabadina parimita samitula kutumbam), idhi "g" yokka swatantra samitulalo sheershaala samitula dwara erpadutundi. swatantra samiti yokka edainaa upasamiti swatantra samiti, kabatti i ("g") vaastavaaniki upasamitulanu teesukoni moosiveyabadutundi.
oka graphloni prati swatantra samiti daani puuraka graphlo oka samuuham, mariyu dheeniki viruddhamgaa untundi. anduvalla, graph yokka swatantra sanklishtata daani puuraka graph yokka click sanklishtataku samanam, mariyu dheeniki viruddhamgaa untundi.
homology samuuhaalu.
aneka mandhi rachayitalu graph "g" = ("v", "e") yokka lakshanaalu mariyu daani swatantra sanklishtata i ("g") yokka homology samuuhaala madhya sambandhaalanu adhyayanam chesaaru. mukhyamgaa, "g" loe aadhipatyam chelaayinche samuuhaalaku sambandhinchina aneka lakshanaalu i ("g") yokka konni taggina homology samuuhaalu chinnavi anie haamii istayi.
1. g yokka "mottam" aadhipatya sankhya ", suutram _ 1 nuu suuchistumdi, idhi" g-"oka samiti" la yokka mottam aadhipatya samiti yokka kaneesa cardinality, antey v yokka prati sheersham "s" yokka sheershaaniki prakkane untundi. suutram _ 2 ayithe suutram _ 3.
2. g loe "v" yokka upasamiti "a" yokka "mottam aadhipatya sankhya", suutram _ 4 gaa suuchimchabadutumdi, idhi oka samiti "s" yokka kaneesa cardinality, antey "a" yokka prati sheersham "s" yokka sheershaaniki prakkane untundi. g yokka "independence domination number", suutram _ 5 nuu suuchistumdi, idhi suutram _ 4 yokka anni swatantra setlapai "a" loe "a", garishtamgaa untundi. suutram _ 7 ayithe, suutram _ 3.
3. g" yokka "aadhipatya sankhya", suutram _ 9 anie suuchimchabadutumdi, idhi g yokka aadhipatya samiti yokka kaneesa cardinality-oka samiti "s" antey v\s yokka prati sheersham "s" yokka sheershaaniki prakkane untundi. suutram _ 10. "g" anedi oka swararekha mariyu suutram _ 11 ayithe suutram _ 3 anie gamaninchandi.
4. g" yokka "prerita saripolika sankhya", suutram _ 13 nuu suuchistumdi, idhi "g" loe prerita saripolika yokka atipedda cardinality-upasamitilo edainaa rendu sheershaalanu anusandhaaninche prati anchunu kaligi unna saripolika. suutram _ 14 vanti "v" yokka upasamiti "a" unte suutram _ 3. idhi paina perkonna 1 mariyu 2 lakshanaala yokka saadhaaraneekarana.
5. i '(" g ") anie suchinchabade g yokka" aadhipatyam laeni swatantra samudaayam "," g "yokka samoohaalalo aadhipatyam chelaayinchani swatantra samuuhaala yokka nairoopya saralamaina samudaayam. spashtamgaa i '("g") anedi i ("g") loe untundi; suutram dwara cherika pataanni soochinchandi. "g" anedi oka theega graph ayithe, appudu prerita pata suutram suutram _ 17 anedi anni suutram _ 18kii sunna avutundi. idhi paina perkonna aasti 3 yokka saadhaaraneekarana.
6. g yokka "fractional starr-domination number", suutram _ 19 nuu suuchistumdi, idhi "g" loe oka fractional starr-dominating sett yokka kaneesa parimaanam. suutram _ 20 ayithe suutram _ 3.
sambandhita bhavanalu.
meshulam aata anedi graph "zii" paie aadabade aata, idhi "zii" yokka swatantra sanklishtata yokka homological connectivitypai takkuva sarihaddunu lekkinchadaaniki upayoginchavacchu.
graph "g" yokka saripolika sanklishtata, m ("g") anie suuchimchabadutumdi, idhi "g" looni saripolikala yokka nairoopya saralamaina sanklishtata. idhi "g" yokka line graph yokka swatantra sanklishtata.
("m", "n")-chess board complexes anedi puurti dwaipaakshika graph "km, n" paie saripole complexes. idhi "m"-dwara-"n" chadarangam palakapai anni setla sthaanaala yokka nairoopya saralamaina sanklishtata, daanipai prati okkati marokariki bedirimpu lekunda rooklanu unchadam saadhyamavutundi.
g yokka click complexes anedi "g" yokka compliment graph yokka independence complexes.

