20.500.12556/DKUM-87584 Distance formula for direct-co-direct product in the case of disconnected factors Direktni-ko-direktni produkt ▫$G\circledast H$▫ grafov ▫$G$▫ in ▫$H$▫ je graf na množizi vozlišč ▫$V(G)\times V(H)$▫. Vozlišči ▫$(g,h)$▫ in ▫$(g',h')$▫ sta sosednji, če je ▫$gg'\in E(G)$▫ in ▫$hh'\in E(H)$▫ ali ▫$gg'\notin E(G)$▫ in ▫$hh'\notin E(H)$▫. Naj bo največ eden izmed faktorjev ▫$G$▫ in ▫$H$▫ povezan. Pokažemo da je razdalja med dvema vozliščema v ▫$G\circledast H$▫ omejena s tri, razen v majhnem številu izjem. Vse izjeme so natančno popisane, kar prinese razdaljno formulo za ▫$G\circledast H$▫. Direct-co-direct product ▫$G\circledast H$▫ of graphs ▫$G$▫ and ▫$H$▫ is a graph on the vertex set ▫$V(G)\times V(H)$▫. Two vertices ▫$(g,h)$▫ and ▫$(g',h')$▫ are adjacent if ▫$gg'\in E(G)$▫ and ▫$hh'\in E(H)$▫ or ▫$gg'\notin E(G)$▫ and ▫$hh'\notin E(H)$▫. We show that if at most one factor of ▫$G\circledast H$▫ is connected, then the distance between two vertices of ▫$G\circledast H$▫ is bounded by three unless some small number of exceptions. All the exceptions are completely described which yields the distance formula. direktni-ko-direktni produkt razdalja ekscentričnost nepovezan graf direct-co-direct product distance eccentricity disconnected graphs direktni-ko-direktni produkt razdalja ekscentričnost nepovezan graf true false true Fakulteta za matematiko, naravoslovje in informacijske tehnologije Angleški jezik Slovenski jezik https://adam-journal.eu/index.php/ADAM/index Članek v reviji 2024-03-21 08:26:41 2024-05-21 09:23:34 2024-05-29 11:37:21 0000-00-00 00:00:00 2023 0 0 art. P2.13 (21 str.) ǂno. ǂ2 ǂVol. ǂ6 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-11-21 2022-09-25 2023-01-04 519.17 136454915 10.26493/2590-9770.1508.8b5 2590-9770 adam_1508.pdf adam_1508.pdf 1 DC46051894A79FA1C2B64354F67CA29D 7444c42ce07144d60b1b155064880759b6942b971bf88ae0c0404f97a3a6e082 57dcec06-1743-11ef-84d7-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=179538 https://adam-journal.eu/index.php/ADAM/article/view/1508 0 5ce7401c-e754-11ee-95b4-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=177183 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0