THE LOCATING RAINBOW EDGE CONNECTION NUMBERS OF SOME GENERALIZED SUN GRAPHS

  • Muhammad Ahnaf Yusuf Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0009-0001-8043-9528
  • A. N. M. Salman Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0001-6895-6234
  • Mukayis Mukayis Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0009-0001-4598-0458
DOI: https://doi.org/10.30598/barekengvol20iss4pp3517-3530
Keywords: Generalized sun graph, Leveled generalized sun graph, Locating rainbow edge coloring, Rainbow code, Rainbow path

Abstract

Throughout this paper, G denotes a finite, simple, connected, and undirected graph. The concept of the locating rainbow edge connection number is motivated by the concept of the locating rainbow connection number in which the coloring is assigned to edges while preserving the locating property. The coloring focuses on determining the smallest natural number k such that there exists a locating rainbow edge -coloring of a graph such that every edge has a distinct rainbow code. In this paper, we define standard generalized sun graphs  and leveled generalized sun graphs . We determine their locating rainbow edge connection numbers. The results are obtained through a theoretical approach and observations of graph structures with rigorous mathematical proofs. The results of Sun(n,p) and depend on their cycle order and the number of bridges.

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Published
2026-08-24
How to Cite
[1]
M. A. Yusuf, A. N. M. Salman, and M. Mukayis, “THE LOCATING RAINBOW EDGE CONNECTION NUMBERS OF SOME GENERALIZED SUN GRAPHS”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 3517-3530, Aug. 2026.
Issue
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2026 Muhammad Ahnaf Yusuf, A. N. M. Salman, Mukayis Mukayis

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