Antimagic valuations of generalized Petersen graphs
نویسندگان
چکیده
A connected graph G is said to be (a, d)-antimagic, for some positive integers a and d, if its edges admit a labeling by the integers 1,2, ... , IE( G) I such that the induced vertex labels consist of an arithmetic progression with the first term a and the common difference d. In this paper we prove that the generalized Petersen graph P(n,2) is (3n2+6, 3)-antimagic for n == 0 (mod 4), n ~ B.
منابع مشابه
On (a, d)-Antimagic Labelings of Generalized Petersen Graphs
A connected graph G = (V, E) is said to be (a, d)antimagic, for some positive integers a and d, if its edges admit a labeling by all the integers in the set {1, 2, . . . , |E(G)|} such that the induced vertex labels, obtained by adding all the labels of the edges adjacent to each vertex, consist of an arithmetic progression with the first term a and the common difference d. Mirka Miller and Mar...
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An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. ...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 22 شماره
صفحات -
تاریخ انتشار 2000