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On the Rainbow Connection Number for Snowflake Graph

1 Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia
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Abstract

Let G be an arbitrary non-trivial connected graph. An edge-colored graph G is called a rainbow connected if any two vertices are connected by a path whose edges have distinct colors, such path is called a rainbow path. The smallest number of colors required to make G rainbow connected is called the rainbow connection number of G, denoted by rc(G). A snowflake graph is a graph obtained by resembling one of the snowflake shapes into vertices and edges so that it forms a simple graph. Let  be a generalized snowflake graph, i.e., a graph with  paths of the stem,  pair of outer leaves,  middle circles, and  pairs of inner leaves. In this paper we determine the rainbow connection number for generalized snowflake graph .

Author Biographies

L

Lyra Yulianti

Indonesia
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia

lecturer in mathematical combinatorics at Andalas University

D

Des Welyyanti

Indonesia
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia

lecturer in mathematical combinatorics at Andalas University

References

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2
Jiang, H., Li, W., Li, X., & Magnant, C. (2021). On proper (strong) rainbow connection of graphs. Discuss. Math. Graph Theory, 41(2), 469-479.
3
Zhu, X., Wei, M., & Magnant, C. (2021). Generalized Rainbow Connection of Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 44(6), 3991-4002.
4
Yulianti, L., Nazra, A., Muhardiansyah, & Narwen. (2021). On the rainbow connection number of triangle-net graph. Journal of Physics: Conference Series, 012004.1836, 2021.
5
Sy, S., Medika, G. H., & Yulianti, L. (2013). The Rainbow Connection of Fan and Sun. Applied Mathematical Sciences, 64th ed.7, HIKARI Ltd: Indonesia, 3155–3159.
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How to Cite

1.
On the Rainbow Connection Number for Snowflake Graph. EKSAKTA [Internet]. 2023 Mar. 30 [cited 2026 Sep. 4];24(01):19-2. Available from: https://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/374

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