This paper is published in Volume-9, Issue-6, 2023
Area
Mathematics
Author
Haoyu Zhang
Org/Univ
Concordia University, Montreal, Canada, Canada
Pub. Date
13 December, 2023
Paper ID
V9I6-1213
Publisher
Keywords
Graph, Domination Number, Burning Number

Citationsacebook

IEEE
Haoyu Zhang. A relationship between the burning number of a graph and its domination number, International Journal of Advance Research, Ideas and Innovations in Technology, www.IJARIIT.com.

APA
Haoyu Zhang (2023). A relationship between the burning number of a graph and its domination number. International Journal of Advance Research, Ideas and Innovations in Technology, 9(6) www.IJARIIT.com.

MLA
Haoyu Zhang. "A relationship between the burning number of a graph and its domination number." International Journal of Advance Research, Ideas and Innovations in Technology 9.6 (2023). www.IJARIIT.com.

Abstract

Graph burning, introduced by Elham Rashanbin in 2016, has gained significant research attention in recent years. This innovative concept involves iteratively selecting nodes in a given graph to 'burn' at each time step. The previously burnt nodes then ignite the adjacent nodes, and this process continues until all nodes are burnt. The minimum number of nodes required to ignite the entire graph is known as the burning number. Similarly, the domination number of a graph refers to the size of the smallest vertex subsets that ensure every vertex in the graph is either part of the subset or adjacent to a vertex within the subset. In this paper, we demonstrate that if the domination number of a graph is at least 6, then its burning number is smaller than or equal to its domination number.