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On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G so that adjacent vertices get labels at least distance two apart and vertices at distance two get distinct labels. A hole is an unused integer within the range of integers used by the labeling. The lambda number of a graphG, denoted λ(G), is the minimum span taken over all L(2,1)-labelings of G. The hole index of a graph G, denoted ρ(G), is the minimum number of holes taken over all L(2,1)-labelings with span exactly λ(G). Georges and Mauro [On the structure of graphs …