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Progress on Roman and Weakly Connected Roman Graphs

Author

Listed:
  • Joanna Raczek

    (Department of Algorithms and Systems Modelling, Faculty of Electronics, Telecommunications and Informatics, Gdańsk Tech, 80-233 Gdańsk, Poland)

  • Rita Zuazua

    (Department of Mathematics, Faculty of Sciences, Universidad Nacional Autónoma de México, Mexico City 4510, Mexico)

Abstract

A graph G for which γ R ( G ) = 2 γ ( G ) is the Roman graph , and if γ R w c ( G ) = 2 γ w c ( G ) , then G is the weakly connected Roman graph . In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. We also study Roman trees improving the result of M.A. Henning’s A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002). Moreover, we give a characterization of weakly connected Roman trees.

Suggested Citation

  • Joanna Raczek & Rita Zuazua, 2021. "Progress on Roman and Weakly Connected Roman Graphs," Mathematics, MDPI, vol. 9(16), pages 1-8, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1846-:d:608755
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