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Abstrakty
In this paper, we study factorizability of C-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) “non-factorizability” of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function.
Czasopismo
Rocznik
Tom
Strony
225--263
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- St. Ambrose University Department of Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA
Bibliografia
- [1] G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, Mathematical Surveys and Monographs, American Mathematical Society, Rhode Island, 2012.
- [2] A. Bondy, U. Murty, Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, 2008.
- [3] F.-R.K. Chung, Spectral Graph Theory, Regional Conference Series in Mathematics, vol. 92, American Mathematical Society, Rhode Island, 1994.
- [4] S.-Y. Chung, Y.-S. Chung, J.-H. Kim, Diffusion and elastic equations on networks, Publ. RIMS 43 (2007), 699-726.
- [5] E. Estrada, The Structure of Complex Networks, Theory and Applications, Oxford University Press, New York, 2012.
- [6] J. Friedman, J.-P. Tillich, Wave equations for graphs and the edge-based Laplacian, Pacific J. Math. 216 (2004), 699-266.
- [7] V. Girault, P.-A. Raviart, Finite element approximation of the Navier-Stokes equations, vol. 749 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1979.
- [8] G.R.C. Godsil, Algebraic Graph Theory, Graduate Texts in Mathematics, Springer, New York, 2001.
- [9] M.O. Jackson, Social and Economic Networks, Princeton University Press, New Jersey, 2008.
- [10] F. Morales, R. Showalter, Interface approximation of Darcy flow in a narrow channel, Math. Methods Appl. Sci. 35 (2012), 182-195.
- [11] F.A. Morales, Homogenization of geological fissured systems with curved non-periodic cracks, Electron. J. Differential Equations 2014 (2014) 189, 1-29.
- [12] F.A. Morales, M.A. Osorio, On the generation of bipartite grids with controlled regularity for 2-d and 3-d simply connected domains, Appl. Anal. Discrete Math. 8 (2014) 173-199.
- [13] L. Orsenigo, Clusters and clustering in biotechnology: Stylised facts, issues and theories, [in:] P. Braunerhjelm, M.P. Feldman (eds), Cluster Genesis, Oxford University Press, 2006, 195-218.
- [14] J. Solomon, PDE approaches to graph analysis, arXiv:1505.00185[cs.DM], 2015.
- [15] M. van Steen, Graph Theory and Complex Networks, an Introduction, Maarten van Steen, Amsterdam, 2010.
- [16] R.J. Wilson, Introduction to Graph Theory, Addison Wesley Longman Limited, Essex CM20 2JE, England, 1996.
Uwagi
EN
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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