On arithmetic deficiency for bicliques

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Title:	On arithmetic deficiency for bicliques
Authors:	Liu, C.-H.a, Wang, T.-M.b, Char, M.-I.a
Contributors:	Department of Applied Mathematics, Tunghai University
Date:	2012
Issue Date:	2013-06-04T08:21:20Z (UTC)
Publisher:	Yantai; China
Abstract:	It is known that edge-magic-ness can be applied to the arrangement of devices of a wireless network, which is a special case of a general concept of arithmetic edge-antimagicness. A graph G with p vertices and q edges is called (a, d)-edge-antimagic if there exists an injective vertex labeling function f: V(G) → {1, 2, ?, p} such that the induced edge labels, which are defined by f(uv) = f(u) + f(v) for each uv ? E(G), form an arithmetic progression {a, a + d, a + 2d, 4-, a + (q 1)d} where d is a positive integer. The (a, d)-edge-antimagic deficiency μ d(G) of a graph G, which is the least integer k such that G is (a, d)-edge-antimagic by modifying the range of the injective vertex labeling function from {1, 2, ?, p} to {1, 2, ?, p + k}. In this article, we completely determine the (a, d)-edge-antimagic deficiency of complete bipartite graphs K m,n, which in particular confirms a conjecture raised by R. Figueroa-Centeno et al. when d = 1. ? 2012 IEEE.
Relation:	2012 International Conference on Systems and Informatics, ICSAI 2012 2012, Article number6223536, Pages 235-238
Appears in Collections:	[應用數學系所] 會議論文

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