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• W1995658966 abstract "Given a positive integer d, an L(d,1)-labeling of a graph G is an assignment of nonnegative integers to its vertices such that adjacent vertices must receive integers at least d apart, and vertices at distance two must receive integers at least one apart. The λd-number of G is the minimum k so that G has an L(d,1)-labeling using labels in {0, 1, …, k}. Informally, an amalgamation of two disjoint graphs G1 and G2 along a fixed graph G0 is the simple graph obtained by identifying the vertices of two induced subgraphs isomorphic to G0, one in G1 and the other in G2. A flower is an amalgamation of two or more cycles along a single vertex. We provide the exact λ2-number of a generalized flower which is the Cartesian product of a path Pn and a flower, or equivalently, an amalgamation of cylindrical rectangular grids along a certain Pn. In the process, we provide general upper bounds for the λd-number of the Cartesian product of Pn and any graph G, using circular L(d+1,1)-labelings of G where the labels {0, 1, …, k} are arranged sequentially in a circle and the distance between two labels is the shortest distance on the circle." @default.
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• W1995658966 date "2015-01-01" @default.
• W1995658966 modified "2023-09-26" @default.
• W1995658966 title "The minimum span ofL(2,1)-labelings of generalized flowers" @default.
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• W1995658966 doi "https://doi.org/10.1016/j.dam.2014.10.010" @default.
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