| Title | Distance two labelling and direct products of graphs |
| Creator | |
| Date Issued | 2008-09-06 |
| Source Publication | Discrete Mathematics
 |
| ISSN | 0012-365X |
| Volume | 308Issue:17Pages:3805-3815 |
| Abstract | An L (2, 1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that vertices at distance two get different numbers and adjacent vertices get numbers which are at least two apart. The L (2, 1)-labelling number of a graph G, λ (G), is the minimum range of labels over all L (2, 1)-labellings of G. Given two graphs G and H, the direct product of G and H is the graph G × H with vertex set V (G) × V (H) in which two vertices (x, y) and (x, y) are adjacent if and only if xx ∈ E (G) and yy ∈ E (H). In this paper, we completely determine the L (2, 1)-labelling numbers of K × K for m, n ≥ 2, and K × P for m ≥ 3, n ≥ 1, where P is the path of length n. The L (2, 1)-labelling numbers of K × C for m ≥ 3 and some special values of n are also determined, where C is the cycle of length n. © 2007 Elsevier B.V. All rights reserved. |
| Keyword | Direct product L (2, 1)-labelling |
| DOI | 10.1016/j.disc.2007.06.046 |
| URL | View source |
| Language | 英语English |
| Scopus ID | 2-s2.0-44149113984 |
| Citation statistics | |
| Document Type | Journal article |
| Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/6658 |
| Collection | Research outside affiliated institution |
| Corresponding Author | Lin，Wensong |
| Affiliation | 1.Department of Mathematics,Southeast University,Nanjing, 210096,China 2.HKBU-BNU International College,Zhuhai,China |
| Recommended Citation GB/T 7714 | Lin，Wensong,Lam，Peter Che Bor. Distance two labelling and direct products of graphs[J]. Discrete Mathematics, 2008, 308(17): 3805-3815. |
| APA | Lin，Wensong, & Lam，Peter Che Bor. (2008). Distance two labelling and direct products of graphs. Discrete Mathematics, 308(17), 3805-3815. |
| MLA | Lin，Wensong,et al."Distance two labelling and direct products of graphs". Discrete Mathematics 308.17(2008): 3805-3815. |
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