Abstract
An analysis of the problem of isomorphism of natural modular graphs is continued. New results are obtained for regular graphs of degree 4. The general approach to the analysis of arbitrary regular NM-graphs is developed, which brings close to solving the isomorphism problem for a given class of numerical graphs.
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G. A. Donets, “Analytically preset graphs,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova AN USSR, Kiev (1987), pp. 20–27.
G. A. Donets, “Optimal coding of homogeneous trees in arithmetic graphs,” in: Methods of Solving Extremum Problems and Adjacent Problems [in Russian], Inst. Kibern. im. V. M. Glushkova AN USSR, Kiev (1987), pp. 72–77.
G. P. Donets’ and Yu. I. Nezhentsev, “Arithmetical graphs and their representation,” Dop. AN URSR, Ser. A, No. 11, 5–8 (1990).
G. A. Donets and I. E. Shulinok, “General representation of numerical graphs,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (2004), pp. 11–18.
I. E. Shulinok, “Connectivity of natural modular graphs,” Cybern. Syst. Analysis, 34,No. 5, 673–675 (1998).
I. E. Shulinok, “Connectivity and cyclomatic number of natural modular graphs,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (1999), pp. 51–57.
G. O. Shulinok, “Isomorphism of natural modular graphs,” in: Theory of Optimal Solutions [in Ukrainian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (2004), pp. 69–73.
G. A. Donets and G. A. Shulinok, “Isomorphism of natural arithmetic graphs,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (2003), pp. 47–53.
G. A. Shulinok, “Isomorphism of regular NM-graphs,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (2005), pp. 100–106.
H. Hasse, Number Theory, Springer-Verlag, New York (1980).
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 95–103, January–February 2006.
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Donets, G.A., Shulinok, G.A. Isomorphism of regular NM-graphs of degree 4. Cybern Syst Anal 42, 83–89 (2006). https://doi.org/10.1007/s10559-006-0040-4
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DOI: https://doi.org/10.1007/s10559-006-0040-4