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)
A. N. M. Salman (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Mukayis Mukayis (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application

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.