Ratnaning Palupi, A.N.M. Salman
Let G be a nontrivial simple connected graph, ab be an edge of G and m be an integer greater than or equal to 3. A path of order m, denoted by pm, is a graph whose vertices can be labelled v1, v2, …, vm such that E(pm) = {v1v2, v2v3, …, vm−1vm}. A Gabm -shield graph is a graph obtained by pm and m − 1 copies of G such that the ab edge of i-th G embedded to i-th edge of pm by embedding a to vi and b to vi+1. A path in a vertexcolored graph is said to be rainbow-vertex path if every internal vertex in the path has different color. A vertex-colored graph is said to be rainbow-vertex connected if for every pair of vertices there exists a rainbow-vertex path connecting them. The rainbow- vertex connection number of G, denoted by rv(G), is the minimum colors needed to make Grainbow-vertex connected. In this paper, we determine the rainbow-vertex connection numbers of of wheel-shield graphs (Wn)bm, specifically finding that the number ranges from m − 2 to m + 1 depending on the order of the wheel. © 2025 Author(s).
Business Administration Study Program, Politeknik Negeri Malang, Jln. Soekarno Hatta No. 9, Malang, 65141, Indonesia; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jln. Ganesa No. 10, Bandung, 40132, Indonesia