- Title
- d-lucky labeling of graphs
- Creator
- Miller, Mirka; Rajasingh, Indra; Emilet, D. Ahima; Jemilet, D. Azubha
- Relation
- 3rd International Conference on Recent Trends in Computing 2015 (ICRTC-2015). 3rd International Conference on Recent Trends in Computing 2015 [presented in Procedia Computer Science, Vol. 57 No. 2015] (12-13 March, 2015 ) p. 766-771
- Publisher Link
- http://dx.doi.org/10.1016/j.procs.2015.07.473
- Publisher
- Elsevier
- Resource Type
- conference paper
- Date
- 2015
- Description
- Let l: V(G) → N be a labeling of the vertices of a graph G by positive integers. Define C(u) = Σv∈N(v)l(v) + d(u), where d(u) denotes the degree of u and N(u) denotes the open neighborhood of u. In this paper we introduce a new labeling called d-lucky labeling and study the same as a vertex coloring problem. We define a labeling l as d-lucky if c(u) ≠ c(v), for every pair of adjacent vertices u and v in G. The d-lucky number of a graph G, denoted by ηdl(G), is the least positive k such that G has a d-lucky labeling with {1,2,...,k} as the set of labels. We obtain ηdl(G) = 2 for hypercube network, butterfly network, benes network, mesh network, hypertree and X-tree.
- Subject
- lucky labeling; d-lucky labeling; benes network; butterfly network; mesh network
- Identifier
- http://hdl.handle.net/1959.13/1329993
- Identifier
- uon:26288
- Identifier
- ISSN:1877-0509
- Rights
- © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
- Language
- eng
- Full Text
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