Burnability of double spiders and path forests
Document Type
Article
Publication Date
2-1-2023
Abstract
The burning number of a graph can be used to measure the spreading speed of contagion in a network. The burning number conjecture is arguably the main unresolved conjecture related to this graph parameter, which can be settled by showing that every tree of order m(2) has burning number at most m. This is known to hold for many classes of trees, including spiders - trees with exactly one vertex of degree greater than two. In fact, it has been verified that certain spiders of order slightly larger than m(2) also have burning numbers at most m, a result that has then been conjectured to be true for all trees. The first focus of this paper is to verify this slightly stronger conjecture for double spiders - trees with two vertices of degrees at least three and they are adjacent. Our other focus concerns the burning numbers of path forests, a class of graphs in which their burning numbers are naturally related to that of spiders and double spiders. Here, our main result shows that a path forest of order m(2) with a sufficiently long shortest path has burning number exactly m, the smallest possible for any path forest of the same order. (C) 2022 Elsevier Inc. All rights reserved.
Keywords
Spread of social contagion, Burning number conjecture, Graph algorithm, Double spider, Path forest
Divisions
MathematicalSciences
Funders
Universiti Sains Malaysia (1001/PMATHS/8011129)
Publication Title
Applied Mathematics and Computation
Volume
438
Publisher
Elsevier
Publisher Location
STE 800, 230 PARK AVE, NEW YORK, NY 10169 USA