The Rainbow Vertex-Connection Number of Star Fan Graphs

Ariestha Widyastuty Bustan, A.N.M. Salman

Abstract


A vertex-colored graph  is said to be rainbow vertex-connected, if for every two vertices  and  in , there exists a  path with all internal vertices have distinct colors. The rainbow vertex connection number of , denoted by is the smallest number of colors needed to make  rainbow vertex connected. In this paper, we determine the rainbow vertex connection number of star fan graphs.


Keywords


graph; rainbow vertex-coloring; rainbow vertex-connection number; star fan graph; fan

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References


R. Diestel, Graph Theory 4th Edition, Springer, 2010.

M. Krivelevich and R. Yuster, "The rainbow connection of a graph is (at reciprocal to its minimum degree," Journal of Graph Theory, Vol. 63, no. 2, pp 185-191, 2010.

X. Li and S. Liu, "Rainbow vertex-connection number of 2-connected graphs," ArXiv preprint arXiv: 1110.5770, 2011.

D. N. Simamora and A. N. M. Salman, "The rainbow (vertex) connection number of pencil graphs," Procedia Computer Science, vol. 74, pp 138-142, 2015.

A. W. Bustan, " Bilangan terhubung titik pelangi untuk graf lingkaran bintang (SmCn)," Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 10, no. 2, pp. 77-81, 2016.




DOI: https://doi.org/10.18860/ca.v5i3.5516

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Copyright (c) 2018 Ariestha Widyastuty Bustan, A.N.M. Salman

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