A study on cyclic bandwidth sum

Ying-Da Chen and Jing-Ho Yan ()
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Ying-Da Chen: Aletheia University
Jing-Ho Yan: Aletheia University

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 18, 295-308

Abstract: Abstract Suppose G is a graph of p vertices. A proper labeling f of G is a one-to-one mapping f:V(G)→{1,2,…,p}. The cyclic bandwidth sum of G with respect to f is defined by CBS f (G)=∑ uv∈E(G)|f(v)−f(u)| p , where |x| p =min {|x|,p−|x|}. The cyclic bandwidth sum of G is defined by CBS(G)=min {CBS f (G): f is a proper labeling of G}. The bandwidth sum of G with respect to f is defined by BS f (G)=∑ uv∈E(G)|f(v)−f(u)|. The bandwidth sum of G is defined by BS(G)=min {BS f (G): f is a proper labeling of G}. In this paper, we give a necessary and sufficient condition for BS(G)=CBS(G), and use this to show that BS(T)=CBS(T) when T is a tree. We also find cyclic bandwidth sums of complete bipartite graphs.

Keywords: Proper labeling; Cyclic bandwidth sum; Complete bipartite graph; Tree; Cyclic displacement; Zero cycle; Extended labeling; Balanced 2-color (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-007-9051-y

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