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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
ANM Salman
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia
Electrical & Electronics Engineering

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Rainbow connection number of comb product of graphs Dinny Fitriani; ANM Salman; Zata Yumni Awanis
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.9

Abstract

An edge-colored graph G is called a rainbow connected if any two vertices are connected by a path whose edges have distinct colors. Such a path is called a rainbow path. The smallest number of colors required in order to make G rainbow connected is called the rainbow connection number of G. For two connected graphs G and H with v ∈ V(H), the comb product between G and H, denoted by G⊳vH, is a graph obtained by taking one copy of G and |V(G)| copies of H and identifying the i-th copy of H at the vertex v to the i-th vertex of G. In this paper, we give sharp lower and upper bounds for the rainbow connection number of comb product between two connected graphs. We also determine the exact values of rainbow connection number of G⊳vH for some connected graphs G and H.
Co-Authors Dinny Fitriani Zata Yumni Awanis