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Burning Numbers of t-unicyclic Graphs

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A Correction to this article was published on 10 January 2022

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Abstract

Given a graph G, the burning number of G is the smallest integer k for which there are vertices \(x_1, x_2,\ldots ,x_k\) such that \((x_1,x_2,\ldots ,x_k)\) is a burning sequence of G. It has been shown that the graph burning problem is NP-complete, even for trees with maximum degree three, or linear forests. A t-unicyclic graph is a unicycle graph in which the unique vertex in the graph with degree greater than two has degree \( t + 2 \). In this paper, we first present the bounds for the burning number of t-unicyclic graphs, and then use the burning numbers of linear forests with at most three components to determine the burning number of all t-unicyclic graphs for \(t\le 2\).

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Acknowledgements

Many thanks to the anonymous referee for his/her many helpful comments and suggestions, which have considerably improved the presentation of the paper.

Funding

Partially supported by NSFC under grant number 11971158.

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, People’s Republic of China

    Ruiting Zhang, Yingying Yu & Huiqing Liu

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  1. Ruiting Zhang
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  2. Yingying Yu
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  3. Huiqing Liu
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Correspondence to Huiqing Liu.

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Communicated by Rosihan M. Ali.

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Zhang, R., Yu, Y. & Liu, H. Burning Numbers of t-unicyclic Graphs. Bull. Malays. Math. Sci. Soc. 45, 417–430 (2022). https://doi.org/10.1007/s40840-021-01194-9

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  • DOI: https://doi.org/10.1007/s40840-021-01194-9

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