Article Sidebar
Submitted
Nov 26, 2022
Accepted
Dec 10, 2022
Published
Mar 30, 2023
Download
Statistic
Read Counter : 236
Download : 195
Downloads
Main Article Content
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 .
Keywords
rainbow connection number
snowflake graph
bridges
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
1.
Yulianti L, Fajri MR, Welyyanti D, Nurinsani A. On the Rainbow Connection Number for Snowflake Graph. EKSAKTA [Internet]. 2023Mar.30 [cited 2025Apr.5];24(01):19-2. Available from: https://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/374
References
- Chartrand, G., Johns, G. L., McKeon, K. A., & Zhang, P. (2008). Rainbow connection in graphs. Mathematica Bohemica, 133(1), 85–98.
- Jiang, H., Li, W., Li, X., & Magnant, C. (2021). On proper (strong) rainbow connection of graphs. Discuss. Math. Graph Theory, 41(2), 469-479.
- Zhu, X., Wei, M., & Magnant, C. (2021). Generalized Rainbow Connection of Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 44(6), 3991-4002.
- Yulianti, L., Nazra, A., Muhardiansyah, & Narwen. (2021). On the rainbow connection number of triangle-net graph. Journal of Physics: Conference Series, 012004.1836, 2021.
- 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.
- Sunil Chandran, L., Issac, D., Lauri, J., & van Leeuwen, E. J. (2022). Upper bounding rainbow connection number by forest number. Discrete Math, 345(7), 112829.
- Maulani, A., Pradini, S., Setyorini, D., & Sugeng, K. A. (2020). Rainbow connection number of Cm o Pn and Cm o Cn. Indonesian Journal of Combinatorics, 3(2), 95–108.
- Rocha, A., Almeida, S. M., & Zatesko, L. M. (2020). The Rainbow Connection Number of Triangular Snake Graphs. Anais do Encontro de Teoria da Computação (ETC), 65–68.
- Fitriani, D., Salman, A., & Awanis, Z. Y. (2022). Rainbow connection number of comb product of graphs. Electronic Journal of Graph Theory and Applications (EJGTA), 10(2), 461–474.
- Chen, L., & Al, E. T. (2018). On various (strong) rainbow connection numbers of graphs. Australasian Journal Of Combinatorics, 70(1), 137–156.
- Helda Mercy, M., & Annammal Arputhamary, I. (2020). A Study on Strong Rainbow Vertex-Connection in Some Classes of Generalized Petersen Graphs. Procedia Comput Sci, 172, 9–15.
- Li, W. jing, Jiang, H., & He, J. bei. (2022). Rainbow and Monochromatic Vertex-connection of Random Graphs. Acta Mathematicae Applicatae Sinica, English Series 2022 38:4, 38(4), 966–972.
- Fauziah, D. A., Dafik, Agustin, I. H., & Alfarisi, R. (2019). The rainbow vertex connection number of edge corona product graphs. IOP Conf Ser Earth Environ Sci, 243(1), 012020.
- Lima, P. T., van Leeuwen, E. J., & van der Wegen, M. (2021). Algorithms for the rainbow vertex coloring problem on graph classes. Theor Comput Sci, 887, 122–142.
- Bai, X. Q., Huang, Z., & Li, X. L. (2022). Bounds for the Rainbow Disconnection Numbers of Graphs. Acta Mathematica Sinica, English Series 2022 38:2, 38(2), 384–396.
- Li, X., & Weng, Y. (2021). Further results on the rainbow vertex-disconnection of graphs. Bull. Malays. Math. Sci. Soc., 44(5), 3445–3460.
- Chen, X. lin, Li, X. liang, & Lian, H. shu. (2020). Rainbow k-connectivity of Random Bipartite Graphs. Acta Mathematicae Applicatae Sinica, English Series 2020 36:4, 36(4), 879–890.
- Bača, M., Salman, A. N. M., Simanjuntak, R., & Susanti, B. H. (2020). Rainbow 2-connectivity of edge-comb product of a cycle and a Hamiltonian graph. Proceedings - Mathematical Sciences 2020 130:1, 130(1), 1–12.
- Hu, Y., & Wei, Y. (2020). Rainbow Antistrong Connection in Tournaments. Graphs and Combinatorics 2020 37:1, 37(1), 167–181.
- al Jabbar, Z. L., Dafik, Adawiyah, R., Albirri, E. R., & Agustin, I. H. (2020). On rainbow antimagic coloring of some special graph. J Phys Conf Ser, 1465(1), 012030.
- B, S., Dafik, S., H, A. I., & R, A. (2020). On Rainbow Antimagic Coloring of Some Graphs. Journal of Physics: Conference Series ICOPAMBS 2019, 1465, 1–8.
- I, K., I, K. A., Dafik, & R, A. (2019). On The Rainbow Antimagic Connection Number of Some Wheel Related Graphs. International Journal of Academic and Applied Research (IJAAR), 12(3), 60–64.
- Budi, H. S., Dafik, Tirta, I. M., Agustin, I. H., & Kristiana, A. I. (2021). On rainbow antimagic coloring of graphs. J Phys Conf Ser, 1832(1), 012016.
- Joedo, J. C., Dafik, Kristiana, A. I., Agustin, I. H., & Nisviasari, R. (2022). On the rainbow antimagic coloring of vertex amalgamation of graphs. J Phys Conf Ser, 2157(1).
- Sulistiyono, B., Slamin, Dafik, Agustin, I. H., & Alfarisi, R. (2020). On rainbow antimagic coloring of some graphs. J Phys Conf Ser, 1465(1).
- Septory, B. J., Utoyo, M. I., Dafik, Sulistiyono, B., & Agustin, I. H. (2021). On rainbow antimagic coloring of special graphs. J Phys Conf Ser, 1836(1), 012016.
- Rinaldi, G. (2021). Regular 1-factorizations of complete graphs and decompositions into pairwise isomorphic rainbow spanning trees. Australasian Journal Of Combinatorics, 80(2), 178–196.
- Glock, S., Kühn, D., Montgomery, R., & Osthus, D. (2021). Decompositions into isomorphic rainbow spanning trees. Journal of Combinatorial Theory, Series B, 146, 439-484.
- Lu, L., Meier, A., & Wang, Z. (2021). Anti-Ramsey number of edge-disjoint rainbow spanning trees in all graphs. arXiv preprint arXiv:2104.12978.
- Li, S., Shi, Y., Tu, J., & Zhao, Y. (2019). On the complexity of k-rainbow cycle colouring problems. Discrete Appl Math (1979), 264, 125–133.
- Brause, C., Jendrol’, S., & Schiermeyer, I. (2021). From Colourful to Rainbow Paths in Graphs: Colouring the Vertices. Graphs and Combinatorics 2021 37:5, 37(5), 1823–1839
- Babiński, S., & Grzesik, A. (2022). Graphs without a rainbow path of length 3. arXiv preprint arXiv:2211.02308.
- Awanis, Z. Y., Salman, A., Saputro, S. W., Bača, M., & Semaničová-Feňovčíková, A. (2020). The strong 3-rainbow index of edge-amalgamation of some graphs. Turkish Journal of Mathematics, 44(2), 446–462.
- Awanis, Z. Y., & Salman, A. N. M. (2019). The 3-rainbow index of amalgamation of some graphs with diameter 2. J Phys Conf Ser, 1127(1), 012058.
- Hastuti, Y., Agustin, I. H., Prihandini, R. M., & Alfarisi, R. (2019). The total rainbow connection on comb product of cycle and path graphs. IOP Conference Series: Earth and Environmental Science, Vol. 243, No. 1, p. 012114.
- Bitterman, A. (2021). The Rainbow Connection: A Time-Series Study of Rainbow Flag Display Across Nine Toronto Neighborhoods. Urban Book Series, 117–137.
- Dafik, Sucianto, B., Irvan, M., & Rohim, M. A. (2019). The Analysis of Student Metacognition Skill in Solving Rainbow Connection Problem under the Implementation of Research-Based Learning Model. International Journal of Instruction, 12(4), 593–610.
- Eiben, E., Ganian, R., & Lauri, J. (2018). On the complexity of rainbow coloring problems. Discrete Appl Math (1979), 246, 38–48
- Fajri, M. R., Fajri, L. H., Ashari, J., Abdurrahman, A., & Arsyad, A. (2022). On the Metric Dimension for Snowflake Graph. EKSAKTA: Berkala Ilmiah Bidang MIPA, 23(04), 275–290.