On the hole index of L(2,1)-labelings of r-regular graphs |
| |
Authors: | Sarah Spence Adams Bradford Westgate |
| |
Institution: | a Franklin W. Olin College of Engineering, Olin Hall, Olin Way, Needham, MA 02492, USA b Mathematics and Sciences Division, Babson College, Babson Park, MA 02457, USA |
| |
Abstract: | 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 graph G, 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 with non-surjective L(2,1)-labelings, SIAM J. Discrete Math. 19 (2005) 208-223] conjectured that if G is an r-regular graph and ρ(G)?1, then ρ(G) must divide r. We show that this conjecture does not hold by providing an infinite number of r-regular graphs G such that ρ(G) and r are relatively prime integers. |
| |
Keywords: | 05C15 05C78 |
本文献已被 ScienceDirect 等数据库收录! |
|