20.500.12556/RUL-134485 On L(d, 1)-labelling of trees Given a graph ▫$G$▫ and a positive integer ▫$d$▫, an ▫$L(d,1)$▫-labelling of ▫$G$▫ is a function ▫$f$▫ that assigns to each vertex of ▫$G$▫ a non-negative integer such that if two vertices ▫$u$▫ and ▫$v$▫ are adjacent, then ▫$|f(u)-f(v) |\ge d$▫ and if ▫$u$▫ and ▫$v$▫ are at distance two, then ▫$|f(u)-f(v)| \ge 1$▫. The ▫$L(d,1)$▫-number of ▫$G$▫, ▫$\lambda_d(G)$▫, is the minimum ▫$m$▫ such that there is an ▫$L(d,1)$▫-labelling of ▫$G$▫ with ▫$f(V) \subseteq \{0,1,\dots , m\}$▫. A tree ▫$T$▫ is of type 1 if ▫$\lambda_d(T) = \Delta+d-1$▫ and is of type 2 if ▫$\lambda_d(T) \ge \Delta+d$▫. This paper provides sufficient conditions for ▫$\lambda_d(T)=\Delta+d-1$▫ generalizing the results of Wang [W. Wang, The ▫$L(2,1)$▫-labeling of trees, Discrete Appl. Math. 154 (2006) 598-603] and Zhai, Lu, and Shu [M. Zhai, C. Lu and J. Shu, A note on ▫$L(2,1)$▫-labeling of Trees, Acta. Math. Appl. Sin. 28 (2012) 395-400] for ▫$L(2,1)$▫-labelling. L(d 1)-labelling tree distance [Delta]-vertex matematika teorija grafov drevo true false true Angleški jezik Slovenski jezik Članek v reviji 2022-01-18 11:14:29 2022-01-18 11:14:33 2022-09-13 03:55:27 0000-00-00 00:00:00 2020 0 0 Str. 87-102 iss. 2 Vol. 5 Spring 2020 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2476-4965 10.22052/mir.2020.227370.1211 20362243 RAZ_Hrastnik_Ladinek_Irena_2020.pdf RAZ_Hrastnik_Ladinek_Irena_2020.pdf 1 DEB215D3F3AD01DD6F4B9FD833317FBD d36d7d50c0c4ea1ebed966924309571b59ab7a69eee3108dc00925418ead4987 4012656a-7847-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=152974 http://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf 0 c42cdb31-7847-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=152976 Fakulteta za strojništvo 0 0 0