Graph Burning and Information Dissemination in Communication Networks

Graph burning is a discrete-time process devised to model the spread of information, contagion or influence across the vertices of a network. At each time step, a single vertex is chosen as a new fire source and all vertices adjacent to already burning vertices become burning in the next step. The burning number of a graph is the fewest rounds needed to burn every vertex, thus quantifying the network’s vulnerability to rapid dissemination. Determining this number is NP-hard, motivating approximation algorithms, heuristics and exact formulations. Beyond its purely theoretical appeal, graph burning informs the design of alert systems in sensor or wireless networks, the analysis of viral marketing strategies in social media and resilience assessment in infrastructure grids. Researchers have explored connections with classical broadcast protocols—where each informed node may communicate to one neighbour per round—and generalisations that incorporate local knowledge or threshold-based influence. The interplay between approximation quality, algorithmic efficiency and network topology remains central, with special attention to trees, grids and other canonical graph families. Recent advances span farthest-first traversal algorithms, integer programming formulations, constraint-programming methods and extensions that model probabilistic or adversarial spreading. This blend of combinatorial theory and practical applicability continues to illuminate how information permeates complex communication topologies under resource or time constraints.

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Graph Burning and Information Dissemination in Communication Networks publication trend

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Technical terms

Graph burning process: A discrete simulation of information spread where, at each round, one new fire source is chosen and existing burning vertices ignite all neighbours in the next step.

Burning number: The minimum number of rounds required to burn all vertices in a graph under the graph burning process.

Burning sequence: An ordered list of vertices chosen as new fire sources at each time step that results in the complete burning of the graph.

Approximation algorithm: An algorithm that produces near-optimal solutions for NP-hard problems within a provable bound of the true optimum.

Independent Cascade model: A stochastic or threshold-based spreading model where influence from burning neighbours must exceed a threshold before a vertex becomes burning.

References

1. Burning Graphs Through Farthest-First Traversal. IEEE Access (2022).
2. Graph Burning: Mathematical Formulations and Optimal Solutions. Mathematics (2022).
3. An Independent Cascade Model of Graph Burning. Symmetry (2023).