Original Research Article

Article volume = 2023 and issue = 2

Pages: 164–166

Article publication Date: November 27, 2023

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# 2-Generalized burning number of square graphs

#### Abolfazl Bahmani(a), Mojgan Emami(a), and Ozra Naserian(b)

(a) Department of Mathematics, University of Zanjan, Zanjan, Iran.

(b) Department of Mathematics, Islamic Azad University, Zanjan, Iran.

##### Abstract:

The burning number of a graph G, denoted by b(G), is the minimum number of steps it takes to burn the graph. 2-Generalized burning number of G which is a generalization of b(G), denoted by b_2(G), is the minimum number of steps it takes to burn every vertex of G by burning vertices only if they are adjacent to at least 2 burned neighbors. In this paper, we give some bounds for the 2-generalized burning number of square graphs. In particular 2-generalized burning number of square graphs for some specific graphs are obtained.

##### Keywords:

2-generalized burning number; Square graph.

##### References:

- [1] J. Ayel and O. Favaron, Helms are graceful in Progress in Graph Theory, Academic Press, Toronto, (1984). 2
- [2] A. Bonato, J. Janssen and E. Roshanbin, Burning a Graph as a Model of Social Contagion, Lecture Notes in Computer Science 8882 (2014) 13-22. 1
- [3] Yinkui Li, Xiaoxiao Qin and Wen Li, The generalized burning number of graphs, Applied Mathematics and Computation 411 (2021) 126306. 1, 1.1, 1.2
- [4] D.B. West, Introduction to Graph Theory, 2nd edition, Prentice Hall, (2001). 1

##### Cite this article as:

- Abolfazl Bahmani, Mojgan Emami, and Ozra Naserian, 2-Generalized burning number of square graphs, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.164–166, 2023
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