Volume 4, Issue 2, June 2018, Page: 54-59
The L(2, 1)-labeling on β-product of Graphs
Kamesh Kumar, Faculty of Mathematics, College of Pharmacy, Teerthanker Mahaveer University, Moradabad (U.P.), India
Received: May 11, 2018;       Accepted: Jun. 1, 2018;       Published: Jul. 3, 2018
DOI: 10.11648/j.ijdst.20180402.13      View  546      Downloads  23
Abstract
The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those vertices at distance two must differ by at least 1. The L(2, 1)-labeling number of G is the smallest number k such that G has an L(2, 1)-labeling with maximum of f(v) is equal to k, where v belongs to vertex set of G. In this paper, upper bound for the L(2, 1)-labeling number for the β-product of two graphs has been obtained in terms of the maximum degrees of the graphs involved.
Keywords
Channel Assignment, L(2, 1)-labeling, L(2, 1)-labeling Number, Graph β-product
To cite this article
Kamesh Kumar, The L(2, 1)-labeling on β-product of Graphs, International Journal on Data Science and Technology. Vol. 4, No. 2, 2018, pp. 54-59. doi: 10.11648/j.ijdst.20180402.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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