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Bandwidth sums of block graphs and cacti

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Abstract

A labeling of a graph G is an injective function f:V(G)→ℤ. The bandwidth sum of a graph G with respect to a labeling f is \(B_{s}^{f}(G) = \sum_{uv \in E(G)} |f(u)-f(v)|\) and the bandwidth sum of G is \(B_{s}(G) = \min\{B_{s}^{f}(G)\colon f\mbox{ is a labeling of }G\}\). In this paper, we determine bandwidth sums for some block graphs and cacti.

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Acknowledgements

The authors thank the referee for many useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, 10617, Taiwan

    Gerard Jennhwa Chang

  2. Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan

    Gerard Jennhwa Chang

  3. Taipei Office, National Center for Theoretical Sciences, Taipei, Taiwan

    Gerard Jennhwa Chang

  4. Department of Applied Mathematics, Aletheia University, Tamsui, 251, Taiwan

    Ma-Lian Chia & Jing-Ho Yan

  5. Department of Applied Mathematics, National Dong Hwa University, Hualien, 97401, Taiwan

    David Kuo & Ji-Yin Lin

Authors
  1. Gerard Jennhwa Chang
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  2. Ma-Lian Chia
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  3. David Kuo
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  4. Ji-Yin Lin
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  5. Jing-Ho Yan
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Corresponding author

Correspondence to Ma-Lian Chia.

Additional information

G.J. Chang is supported in part by the National Science Council under grant NSC98-2115-M-002-013-MY3. M.-L. Chia is supported in part by the National Science Council under grants NSC97-2115-M-156-004-MY2. D. Kuo is supported in part by the National Science Council under grants NSC94-2115-M-259-004. J.-H. Yan is supported in part by the National Science Council under grants NSC94-2115-M-156-001.

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Chang, G.J., Chia, ML., Kuo, D. et al. Bandwidth sums of block graphs and cacti. J Comb Optim 27, 679–687 (2014). https://doi.org/10.1007/s10878-012-9548-x

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  • DOI: https://doi.org/10.1007/s10878-012-9548-x

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