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All Journal Emerging Science Journal
Pritta E. Putri
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat,
Environmental Science

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On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs Ariestha W. Bustan; A. N. M. Salman; Pritta E. Putri; Zata Y. Awanis
Emerging Science Journal Vol 7, No 4 (2023): August
Publisher : Ital Publication

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28991/ESJ-2023-07-04-016

Abstract

Locating the rainbow connection number of graphs is a new mathematical concept that combines the concepts of the rainbow vertex coloring and the partition dimension. In this research, we determine the lower and upper bounds of the locating rainbow connection number of a graph and provide the characterization of graphs with the locating rainbow connection number equal to its upper and lower bounds to restrict the upper and lower bounds of the locating rainbow connection number of a graph. We also found the locating rainbow connection number of trees and regular bipartite graphs. The method used in this study is a deductive method that begins with a literature study related to relevant previous research concepts and results, making hypotheses, conducting proofs, and drawing conclusions. This research concludes that only path graphs with orders 2, 3, 4, and complete graphs have a locating rainbow connection number equal to 2 and the order of graph G, respectively. We also showed that the locating rainbow connection number of bipartite regular graphs is in the range of r-⌊n/4⌋+2 to n/2+1, and the locating rainbow connection number of a tree is determined based on the maximum number of pendants or the maximum number of internal vertices. Doi: 10.28991/ESJ-2023-07-04-016 Full Text: PDF
Co-Authors A. N. M. Salman Ariestha W. Bustan Zata Y. Awanis