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Dual Connectivity in Graphs

Author

Listed:
  • Mohammed A. Mutar

    (Department of Mathematics, College of Science, University of Al Qadisiyah, Diwaniyah 58001, Iraq)

  • Daniele Ettore Otera

    (Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, 08412 Vilnius, Lithuania)

  • Hasan A. Khawwan

    (Education Directorate of Al-Qadisiyah, Diwaniyah 58001, Iraq)

Abstract

An edge-coloring σ of a connected graph G is called rainbow if there exists a rainbow path connecting any pair of vertices. In contrast, σ is monochromatic if there is a monochromatic path between any two vertices. Some graphs can admit a coloring which is simultaneously rainbow and monochromatic; for instance, any coloring of K n is rainbow and monochromatic. This paper refers to such a coloring as dual coloring. We investigate dual coloring on various graphs and raise some questions about the sufficient conditions for connected graphs to be dual connected.

Suggested Citation

  • Mohammed A. Mutar & Daniele Ettore Otera & Hasan A. Khawwan, 2025. "Dual Connectivity in Graphs," Mathematics, MDPI, vol. 13(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:229-:d:1564776
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