Abstract
An -labeling of a graph is a function assigning a nonnegative integer to each vertex such that adjacent vertices are labeled with integers differing by at least 2 and vertices at distance two are labeled with integers differing by at least 1. The minimum span across all -labelings of is denoted . An -labeling of and the number are defined analogously, with the additional restriction that the labelings must be injective. We determine when is a join-page amalgamation of graphs, which is defined as follows: given , is obtained from the pairwise disjoint union of graphs by adding all the edges between a vertex in and a vertex in for . Motivated by these join-page amalgamations and the partial relationships between and for general graphs provided by Chang and Kuo, we go on to show that , where is the number of vertices in .
Citation
Nathaniel Karst. Jessica Oehrlein. Denise Sakai Troxell. Junjie Zhu. "On distance labelings of amalgamations and injective labelings of general graphs." Involve 8 (3) 535 - 540, 2015. https://doi.org/10.2140/involve.2015.8.535
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