TY - JOUR
T1 - Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs
AU - Phanalasy, Oudone
AU - Miller, Mirka
AU - Iliopoulos, Costas S.
AU - Pissis, Solon P.
AU - Vaezpour, Elaheh
PY - 2011/3/1
Y1 - 2011/3/1
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 K2, is antimagic. Recently, using completely separating systems, Phanalasy et al. showed that for each k ≥ 2, q ≥(k+12) with k{pipe}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 K2, is antimagic. Recently, using completely separating systems, Phanalasy et al. showed that for each k ≥ 2, q ≥(k+12) with k{pipe}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.
KW - Antimagic graph labeling
KW - Cartesian product of graphs
KW - Completely separating systems
KW - Regular graph
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U2 - 10.1007/s11786-011-0084-3
DO - 10.1007/s11786-011-0084-3
M3 - Article
AN - SCOPUS:81955167487
SN - 1661-8270
VL - 5
SP - 81
EP - 87
JO - Mathematics in Computer Science
JF - Mathematics in Computer Science
IS - 1
ER -