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:	Olayide Ajayi,Deborah, Adefokun,Charles
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2014
Materias:	L(1,1)-labeling D-2 Coloring Direct Product of Graphs Cross Product of Graphs Path and Cycle.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400002
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spelling	oai:scielo:S0716-091720140004000022015-01-19L(1,1)-Labeling of Direct Product of any Path and CycleOlayide Ajayi,DeborahAdefokun,Charles L(1,1)-labeling D-2 Coloring Direct Product of Graphs Cross Product of Graphs 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 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.33 n.4 20142014-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400002en10.4067/S0716-09172014000400002
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	L(1,1)-labeling D-2 Coloring Direct Product of Graphs Cross Product of Graphs Path and Cycle.
spellingShingle	L(1,1)-labeling D-2 Coloring Direct Product of Graphs Cross Product of Graphs Path and Cycle. Olayide Ajayi,Deborah Adefokun,Charles L(1,1)-Labeling of Direct Product of any Path and Cycle
description	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.
author	Olayide Ajayi,Deborah Adefokun,Charles
author_facet	Olayide Ajayi,Deborah Adefokun,Charles
author_sort	Olayide Ajayi,Deborah
title	L(1,1)-Labeling of Direct Product of any Path and Cycle
title_short	L(1,1)-Labeling of Direct Product of any Path and Cycle
title_full	L(1,1)-Labeling of Direct Product of any Path and Cycle
title_fullStr	L(1,1)-Labeling of Direct Product of any Path and Cycle
title_full_unstemmed	L(1,1)-Labeling of Direct Product of any Path and Cycle
title_sort	l(1,1)-labeling of direct product of any path and cycle
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2014
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400002
work_keys_str_mv	AT olayideajayideborah l11labelingofdirectproductofanypathandcycle AT adefokuncharles l11labelingofdirectproductofanypathandcycle
_version_	1718439800663441408

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

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