L(d,1) – labeling of join of path and cycle and join of complete graph with path and cycle

Author:
JAYA AMBIGAVATHI RAGAVAN
Affiliation:
Keyword:
L(d,1)-labeling, λd-number, join of two graphs.
Issue Date:
December 2013
Abstract:

Given a graph G and a positive integer d, an L(d, 1)-labeling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then f (u)  f (v)  d ; if u and v are not adjacent but there is a two-edge path between them, then f (u)  f (v )  1. The L(d, 1)-number of G,    d G , is defined as the minimum m such that there is an L(d, 1)-labeling f of G with f(V) {0, 1, 2,…, m}. Motivated by the channel assignment problem introduced by Hale, the L(2, 1)-labeling and the L(1, 1)-labeling (as d=2 and 1, respectively) have been studied extensively in the past decade. This article extends the study to all positive integers d.The aim of this paper is to determine the λd-number of the join of path and cycle and two graphs, Km + Pn and Km + Cn .

Pages:
ISSN:
2319-8044 (Online) - 2231-346X (Print)
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Copy the following to cite this article:

JAYA AMBIGAVATHI RAGAVAN, "L(d,1) – labeling of join of path and cycle and join of complete graph with path and cycle", Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 3, Page Number , 2016

Copy the following to cite this URL:

JAYA AMBIGAVATHI RAGAVAN, "L(d,1) – labeling of join of path and cycle and join of complete graph with path and cycle", Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 3, Page Number , 2016

Available from: https://www.ultrascientist.org/paper/183/

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