Optimal L(d,1)-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over Cycles
Year: 2024
Type: article
Abstract: 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.
Source: Mathematics
DOI: 10.3390/math12193121
Author: Irena Hrastnik Ladinek
Institution: University of Maribor
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4403172188