Dual Connectivity in Graphs

Mohammed A. Mutar, Daniele Ettore Otera () and Hasan A. Khawwan
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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

Mathematics, 2025, vol. 13, issue 2, 1-10

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.

Keywords: edge coloring; rainbow coloring; monochromatic coloring; dual connected graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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