L(1,1)-Labeling of Direct Product of any Path and Cycle
Suppose that [n] = {0, 1, 2,...,n} is a set of non-negative integers and h,k G [n].The L (h, k)-labeling of graph G is the function l : V(G) - [n] such that |l(u) - l(v)| > h if the distance d(u,v) between u and v is 1 and |l(u) - l(v)| > k if d(u,v) = 2. Let L(V(G)) = {l(v): v G V(G)} and let...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2014
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400002 |
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| Sumario: | Suppose that [n] = {0, 1, 2,...,n} is a set of non-negative integers and h,k G [n].The L (h, k)-labeling of graph G is the function l : V(G) - [n] such that |l(u) - l(v)| > h if the distance d(u,v) between u and v is 1 and |l(u) - l(v)| > k if d(u,v) = 2. Let L(V(G)) = {l(v): v G V(G)} and let p be the maximum value of L(V(G)). Then p is called Xi^-number of G if p is the least possible member of [n] such that G maintains an L(h, k) - labeling. In this paper, we establish X} - numbers of Pm X Pn and Pm X Cn graphs for all m,n > 2. |
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