L(1,1)-Labeling of Direct Product of any Path and cycle

• Olayide Ajayi, Deborah ^[1] ; Adefokun, Charles ^[2]
  1. [1] University of Ibadan

     University of Ibadan

     Nigeria

     
  2. [2] Crawford University

     Crawford University

     Nigeria

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 4, 2014, págs. 369-388
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000400002
• Enlaces
  • Texto completo
• Resumen

  • 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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