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On graphs with the maximum edge metric dimensionZhu, Enqiang ...Povezavni metrični generator povezanega grafa ▫$G$▫ je podmnožica vozlišč ▫$S$▫, za katero imata poljubni dve različni povezavi grafa ▫$G$▫ različno razdaljo do nekega vozlišča iz ▫$S$▫; pri tem je ... razdalja med vozliščem ▫$v$▫ in povezavo ▫$e$▫ definirana kot minimum razdalj med ▫$v$▫ in krajiščema povezave ▫$e$▫ v grafu ▫$G$▫. Moč najmanjšega povezavnega metričnega generatorja je povezavna metrična dimenzija, označimo jo z ▫$\dim_e(G)$▫. Za poljuben graf ▫$G$▫ reda ▫$n$▫ je ▫$1 \leq \dim_e(G) \leq n-1$▫. Graf, katerega povezavna metrična dimenzija doseže zgornjo mejo, imenujemo zvrhan. V tem članku so podani karakterizacija strukture zvrhanih grafov ter zadostni in potrebni pogoji za to, da je graf zvrhan. Z uporabo teh rezultatov je podan algoritem, ki v času ▫$O(n^3)$▫ preveri, ali je podani graf reda ▫$n$▫ zvrhan ali ni. Opisana in proučevana je tudi zanimiva družina zvrhanih grafov, katerih nadgrafi dobljeni z dodajanjem ene povezave niso zvrhani.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 257, March 2019, str. 317-324)Type of material - article, component part ; adult, seriousPublish date - 2019Language - englishCOBISS.SI-ID - 18584665
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Database name | Field | Year |
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Zhu, Enqiang | ![]() |
Taranenko, Andrej | 21821 |
Shao, Zehui | ![]() |
Xu, Jin | ![]() |
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