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

doi:10.28991/ESJ-2023-07-04-016

Authors

Ariestha W. Bustan 1) Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat, Indonesia. 2) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Pasifik Morotai, Jl Siswa Darame, Kabupaten Pulau Morotai, Maluku Utara,, Indonesia
A. N. M. Salman
msalman@itb.ac.id
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat,, Indonesia
Pritta E. Putri Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat,, Indonesia
Zata Y. Awanis Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Mataram,, Indonesia

Vol. 7 No. 4 (2023): August

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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-âŒŠn/4âŒ‹+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

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Bustan, A. W., Salman, A. N. M., Putri, P. E., & Awanis, Z. Y. (2023). On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs. Emerging Science Journal, 7(4), 1260–1273. https://doi.org/10.28991/ESJ-2023-07-04-016

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On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs

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