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On fractal cubic network graphs
(Elsevier, 2025-03) Altintas Tankul, Ayse Nur; Selcuk, Burhan; Turan, Muhammed Kamil
The fractal cubic network graphs (FCNG), previously studied by Karci and Selcuk (2015), are reviewed in this paper. First, general information about FCNG is provided, and new topological properties of FCNG are presented. Simulations of the topological properties of FCNG, hypercube, and 2D square meshes have been performed, and the results are introduced. Secondly, a strategy for the routing problem for FCNG is presented. A new strategy for the routing path of FCNG is presented and explained with an example, and a recursive algorithm using this strategy is presented. Thirdly, a strategy for the shortest path problem for FCNG with a similar routing strategy is also presented, and a recursive algorithm for this strategy is given. An algorithm for mapping network nodes on a 2D plane and an algorithm for computing the minimum distance connection point between fractals used to construct the shortest path are also provided. These algorithms are illustrated with an example. The running times of the algorithms are also calculated.