Minggu, 29 Juni 2014 - 21:03:58 WIB
Edge-antimagic Total Labeling of Disjoint Union of Caterpillars
Martin Baca, Dafik, Mirka Miller, Joe Ryan, The Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 61-70
Jurnal Internasional

Abstract

Abstract: Let G = (V,E) be a finite graph, where V (G) and E(G) are the (nonempty) sets of vertices and edges of G. An (a, d)-edge-antimagic total labeling is a bijection f from V (G) U E(G) to the set of consecutive integers {1, 2, . . . , |V (G)| + |E(G)|} with the property that the set of all the edge weights, w(uv) = f(u)+ f(uv)+ f(v), uv in E(G), is {a, a+d, a+2d, . . . , a+ (|E(G)| − 1)d}, for two fixed integers a > 0 and d >= 0. Such a labeling is super if the smallest possible labels appear on the vertices. In this paper we investigate the existence of super (a, d)-edge-antimagic total labelings for
disjoint union of multiple copies of a regular caterpillar.

Key Words: Super (a, d)-edge-antimagic total labelings, disjoint union, regular caterpillar


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