Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs

Oudone Phanalasy, Mirka Miller, CostasS. Iliopoulos, Solon Pissis, Elaheh Vaezpour

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

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.
Original languageUndefined/Unknown
Pages (from-to)81-87
Number of pages7
JournalMathematics in Computer Science
Volume5
Issue number1
DOIs
Publication statusPublished - Mar 2011

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