Construction of antimagic labeling for the Cartesian product of regular graphs

Title: Construction of antimagic labeling for the Cartesian product of regular graphs
Creator: Phanalasy, Oudone; Miller, Mirka; Iliopoulos, Costas S.; Pissis, Solon P.; Vaezpour, Elaheh
Relation: Mathematics in Computer Science Vol. 5, Issue 1, p. 81-87
Publisher Link: http://dx.doi.org/10.1007/s11786-011-0084-3
Publisher: Birkhaeuser Science
Resource Type: journal article
Date: 2011
Description: An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, . . . , q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that that every connected graph, except K 2, is antimagic. Recently, using completely separating systems, Phanalasy et al. showed that for each k≥2,q≥(k+12) with k|2q, there exists an antimagic k-regular graph with q edges and p = 2q/k vertices. In this paper we prove constructively that certain families of Cartesian products of regular graphs are antimagic.
Subject: antimagic graph labeling; regular graph; completely separating systems; Cartesian product of graphs
Identifier: http://hdl.handle.net/1959.13/1053602
Identifier: uon:15630
Identifier: ISSN:1661-8270
Language: eng
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