Vertex-antimagic labelings of regular graphs

Ali Ahmad, Kashif Ali, Martin Bača, Petr Kovář, Andrea Semaničová-Feňovčíková

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

7 Citas (Scopus)


Let G = (V,E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, ..., p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, ..., r + 1.

Idioma originalInglés
Páginas (desde-hasta)1865-1874
Número de páginas10
PublicaciónActa Mathematica Sinica, English Series
EstadoPublicada - sep. 2012
Publicado de forma externa


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