TY - JOUR

T1 - Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs

AU - Phanalasy, Oudone

AU - Miller, Mirka

AU - Iliopoulos, CostasS.

AU - Pissis, Solon

AU - Vaezpour, Elaheh

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

U2 - 10.1007/s11786-011-0084-3

DO - 10.1007/s11786-011-0084-3

M3 - Article

SN - 1661-8270

VL - 5

SP - 81

EP - 87

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

IS - 1

ER -