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A study on cyclic bandwidth sum

Author

Listed:
  • Ying-Da Chen

    (Aletheia University)

  • Jing-Ho Yan

    (Aletheia University)

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.

Suggested Citation

  • Ying-Da Chen & Jing-Ho Yan, 2007. "A study on cyclic bandwidth sum," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 295-308, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9051-y
    DOI: 10.1007/s10878-007-9051-y
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    Cited by:

    1. Rodriguez-Tello, Eduardo & Lardeux, Frédéric & Duarte, Abraham & Narvaez-Teran, Valentina, 2019. "Alternative evaluation functions for the cyclic bandwidth sum problem," European Journal of Operational Research, Elsevier, vol. 273(3), pages 904-919.

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