Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications

Rainbow connection number of comb product of graphs

Dinny Fitriani (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia)
ANM Salman (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia)
Zata Yumni Awanis (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Jalan Majapahit No. 62, Mataram 83125, Indonesia)

Article Info

Publish Date
25 Sep 2022

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.

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Journal Info
Electronic Journal of Graph Theory and Applications (EJGTA)
Website

Abbrev

ejgta

Publisher

Indonesian Combinatorial Society

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...