TY - JOUR

T1 - Vertex magic total labeling of products of cycles

AU - Froncek, Dalibor

AU - Kovář, Petr

AU - Kovářová, Tereza

PY - 2005/12/1

Y1 - 2005/12/1

N2 - A vertex magic total labeling of a graph G(V, E) assigns to all vertices and edges of G labels from the set{1, 2,..., |V|+|E|} so that the sum (called the weight) of the vertex label and of labels of all adjacent edges does not depend on the vertex. A generalized (s, d)-vertex antimagic. total labeling of G assigns positive integers to all vertices and edges of G so that the vertex weights form an arithmetic progression s,s + d,..., s + (|V|- 1)d. We present a construction of vertex magic total labelings of products of cycles Cm x Cn for m,n ≥ 3, n odd. The construction is based on a generalized (s, d)-vertex antimagic labeling of cycles in which non- consecutive integers are used.

AB - A vertex magic total labeling of a graph G(V, E) assigns to all vertices and edges of G labels from the set{1, 2,..., |V|+|E|} so that the sum (called the weight) of the vertex label and of labels of all adjacent edges does not depend on the vertex. A generalized (s, d)-vertex antimagic. total labeling of G assigns positive integers to all vertices and edges of G so that the vertex weights form an arithmetic progression s,s + d,..., s + (|V|- 1)d. We present a construction of vertex magic total labelings of products of cycles Cm x Cn for m,n ≥ 3, n odd. The construction is based on a generalized (s, d)-vertex antimagic labeling of cycles in which non- consecutive integers are used.

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M3 - Article

AN - SCOPUS:67349108214

SN - 1034-4942

VL - 33

SP - 169

EP - 181

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

ER -