Web10 Jan 2024 · Although they mention that the burning number generalises naturally to directed graphs, no further research on this has been done. Here, we introduce graph … Webupper and lower bounds have been established for various well-known graph classes including generalized Petersen graphs [22], p-caterpillars [14], graph products [21], dense and tree-like graphs [16] and theta ... showed that the burning number of a graph is approximable within a factor of 3 for general graphs and 2 for trees. They gave a ...

EconPapers: The generalized burning number of graphs

Web15 Nov 2024 · The burning numberof a graph G, denoted by b(G), is the minimum number of steps needed for the process to end. Note that with our notation, b(G)=T. Suppose that in the process of burning a graph G, we eventually burned the whole graph in ksteps, and for each i(1 ≤ i ≤ k), we denote the vertex that we burn in the ith step by xi. immortals fenyx rising hephaistos vault

Approximation Algorithms for Graph Burning

Web11 Apr 2024 · Graph Burning asks, given a graph G = (V,E) and an integer k, whether there exists (b_ {0},\dots ,b_ {k-1}) \in V^ {k} such that every vertex in G has distance at most i … Web24 Jun 2016 · The original burning number is revisited and analyzed for binomial random graphs, random geometric graphs, and the Cartesian product of paths, and new variants of the burning number are introduced in which a burning sequence of vertices is selected according to some probabilistic rules. 26 PDF Burning a graph is hard Web20 May 2024 · The burning number of the graph is 3, as the graph does not have burning sequence of length less than 3. Fig. 1 An example graph, The vertex sequence [4,7,1] is an optimal burning sequence. The burning number of the graph is 3 Full size image There are a few problems related to graph burning proposed in the literature. list of university in gisborne nz