20.500.12556/DKUM-92050 Optimal L(d,1)-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over Cycles An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where d≥1. The span of f is the difference between the largest and the smallest numbers in f(V). The λ1d-number of G, denoted by λ1d(G), is the minimum span over all L(d,1)-labelings of G. We prove that λ1d(X)≤2d+2, with equality if 1≤d≤4, for direct graph bundle X=Cm×σℓCn and Cartesian graph bundle X=Cm□σℓCn, if certain conditions are imposed on the lengths of the cycles and on the cyclic ℓ-shift σℓ. L(d 1)-labeling λ d 1 -number direct product of graph direct graph bundle Cartesian product of graph Cartesian graph bundle cyclic ℓ-shift channel assignment neposredni produkt grafa direktni produkt grafov grafovski svežnji kartezični produkt grafov kartezični grafovski sveženj ciklični ℓ-premik dodeljevanje kanalov true false true MDPI AG Angleški jezik Slovenski jezik https://www.mdpi.com/journal/mathematics © 2024 by the author Članek v reviji 2025-03-13 11:09:04 2025-03-13 11:09:04 2025-03-14 03:27:41 0000-00-00 00:00:00 2024 0 0 str. 3121 no. 19 Vol. 12 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-09-02 2024-10-04 2024-10-05 519.17 2227-7390 214025731 https://dx.doi.org/10.3390/math12193121 mathematics-12-03121-v2.pdf mathematics-12-03121-v2.pdf 1 E2C87FFDF4798C5A8C4E7C30163D8C22 963ac40051995c8036f1714fbf92238ef5d8c46040827a1f56be28ed4248ea46 ded2970a-fff5-11ef-82d0-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=189246 https://www.mdpi.com/2227-7390/12/19/3121 0 02c9b510-fff5-11ef-82d0-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=189245 Fakulteta za strojništvo 0 0 0