Abstract
In this paper, we consider a class of connected planar 3-regular graphs (rotation systems) and show that, for any two such graphs with the same number of vertices, one kind of local rewriting rule is capable of rewriting one graph to the other. On the basis of such graph development systems, emergent systems including self-organizing systems will be considered in a uniform manner.
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References
Bolognesi, T.: Planar Trivalent Network Computation. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 146–157. Springer, Heidelberg (2007)
Diestel, R.: Graph Theory, 4th edn. Springer, Heidelberg (2010)
Greenlaw, R., Petreschi, R.: Cubic graphs. ACM Computing Surveys 27(4), 471–495 (1995)
Gross, T., Sayama, H. (eds.): Adaptive Networks: Theory. Models and Applications. Springer, Heidelberg (2009)
Milner, R.: The Space and Motion of Communicating Agents. Cambridge University Press (2009)
Rozenberg, R. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific (1997)
Tomita, K., Kurokawa, H., Murata, S.: Graph automata: natural expression of self-reproduction. Physica D 171(4), 197–210 (2002)
Tomita, K., Kurokawa, H.: On the reachability of a version of graph-rewriting system. Information Processing Letters 109(14), 777–782 (2009)
von Neumann, J.: Theory of Self-Reproducing Automata. Univ. of Illinois Press (1966)
Wolfram, S.: A New Kind of Science. Wolfram Media (2002)
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Tomita, K., Ikeda, Y., Hosono, C. (2011). On Rewriting of Planar 3-Regular Graphs. In: Abd Manaf, A., Sahibuddin, S., Ahmad, R., Mohd Daud, S., El-Qawasmeh, E. (eds) Informatics Engineering and Information Science. ICIEIS 2011. Communications in Computer and Information Science, vol 253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25462-8_30
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DOI: https://doi.org/10.1007/978-3-642-25462-8_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25461-1
Online ISBN: 978-3-642-25462-8
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