Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

THE RAINBOW VERTEX-CONNECTION NUMBERS OF WHEEL-SHIELD GRAPHS

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  • Ratnaning Palupi,
  • A. N. M. Salman
Ratnaning Palupi
Business Administration Study Program, Politeknik Negeri Malang, Indonesia
A. N. M. Salman
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss4pp2377-2390
Published September 1, 2025
Keywords
  • Rainbow Vertex Connection Number,
  • Shield Graph,
  • Wheel
How to Cite
[1]
R. Palupi and A. N. M. Salman, “THE RAINBOW VERTEX-CONNECTION NUMBERS OF WHEEL-SHIELD GRAPHS”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2377-2390, Sep. 2025.

Copyright (c) 2025 Ratnaning Palupi, A.N.M. Salman

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

Let  be a nontrivial simple connected graph,  be an edge of  and  be an integer greater than or equal to . A path of order , denoted by , is a graph whose vertices can be labelled  such that . A -shield graph is a graph obtained by  and  copies of  such that the  edge of -th  embedded to -th edge of  by embedding  to  and  to . A path in a vertex-colored 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 , denoted by , is the minimum colors needed to make  rainbow-vertex connected. In this paper, we determine the rainbow-vertex connection numbers of of wheel-shield graphs , specifically finding that the number ranges from  to  depending on the order of the wheel.

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