Burning number of path and cycle related graphs

Jenifer, M. S. Mary; Shanthi, A. S.

doi:10.47974/JDMSC-2582

Open Access Research Article

Burning number of path and cycle related graphs

^*M. S. Mary JeniferCorresponding author23dmtf001@stellamariscollege.edu.inDepartment of MathematicsStella Maris College(Affiliated to University of Madras)Cathedral Road, Chennai, 600086, India0009-0000-7751-9431View full profile → , A. S. Shanthishanthi.a.s@stellamariscollege.edu.inDepartment of MathematicsStella Maris College(Affiliated to University of Madras)Cathedral Road, Chennai, 600086, India0009-0005-0133-1535View full profile →

* Corresponding author · click or hover a name for details

pp. 1347–1354Vol. 29Issue 3March 2026DOI: 10.47974/JDMSC-2582 Crossmark XML

Received:: 19 Mar 2025
Published Online:: 02 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2582
Pages:: 1347–1354

Abstract

In network theory the circulation of data is modelled into a graph and the idea of graph burning is applied. Graph burning is the concept of finding the minimum number of moves that takes for the propagation of data in a network. Even in the cases of memes passed in social media platforms like Facebook and Instagram how quickly an information reaches its followers and the impact of it which affects the entire network can be determined by finding the burning number of the network. In this paper we have determined the burning number of a graph which has path attached with a graph which has diameter 2, flower network and sunlet graph.

Keywords

Burning Cycle Diameter Flower network Sunlet

Subject Classifications

05C9005C99

References

[1] J. Balogh, B. Bollobas and R. Morris, Graph bootstrap percolation, Random Structures and Algorithms, vol. 41, no.4, pp.413-440 (2012).
[2] A. Barghi and P. Winkler, Firefighting on a random geometric graph, Random Structures and Algorithms, vol. 46, no.3, pp. 466-477 (2013).
[3] M. Basher, Even vertex odd mean labeling of some cycle related graphs, Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no.8, pp. 2321–2340 (2021).
[4] A. Bonato, J. Janssen, and E. Roshanbin, Burning a Graph as a Model of Social Contagion, Lecture Notes in Computer Science, vol. 8882, pp. 13–22 (2014).
[5] Debajyoti Mondal, N. Parthiban, V. Kavitha and Indira Rajasingh, APX hardness and Approximation for the k-Burning Number Problem Walcom: Algorithms and Computation, vol. 12635, pp. 283 - 294 (2021).
[6] J. Garcia-Diaz, L. M. X. Rodriguez-Henriquez, J. C. Perez-Sansalvador, and S. E. Pomares-Hernandez, “Graph Burning: Mathematical Formulations and Optimal Solutions,” Mathematics, vol. 10, pp. 2777 (2022).
[7] Jiaqi Song, Xing Qi, and Zhulou Cao, An Independent Cascade Model of Graph Burning, Symmetry, vol. 15, pp. 1527 (2023).
[8] Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics vol. 25, pp. 4-623 (2022).
[9] Mohamed Omar and Vibha Rohilla, Burning Graph Classess, Graphs and Combinatorics, vol. 38 (2022).
[10] N. Nilay and E. Akyar, “Burning number of Jahangir graphs,” Asian Europena Journal of Mathematics, vol. 16, pp. 2350177 (2023).
[11] R. K. Gautam, A. S. Kare, and D. Bhavani, “Faster heuristics for graph burning,” Applied Intelligence, vol. 52, pp.1351-1361 (2022).
[12] S. Sumathi and G. H. Grace, “Selection of activators in finding the burning number,” AKCE International Journal of Graphs and Combinatorics, vol. 20, pp. 115-119 (2023).
[13] I. S. Kumala and A. N. M. Salman, “The rainbow connection number of a flower graph (Cm, Kn) graph and a flower (C3, Fn) graph,”, Procedia Computer Science, vol. 74, pp. 168- 172 (2015).
[14] Yasuaki Kobayashi and Yota Otachi, Parameterized Complexity of Graph Burning, vol. 84, pp. 2379-2393 (2022).
[15] Yinkui Li, Xiaoxiao Qin, and Wen Li, The generalized burning number of graphs, Applied Mathematics and Computation, vol. 411 (2021).
[16] Wen Li, Graphs with burning number equal three, International Journal of Research Granthaalayah, vol. 11, pp. 145-150 (2023).

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