The tau constant and the discrete Laplacian matrix of a metrized graph

European Journal of Combinatorics

Volumn 32, Issue 4, 2011, Pages 639-655

  Cinkir, Zubeyir ^a  

^a ZIRVE UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79951776766     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2011.01.008     Document Type: Article

References (21)

1. M. Baker, X. Faber, Metrized graphs, Laplacian operators, and electrical networks, in: G. Berkolaiko, R. Carlson, S.A. Fulling, P. Kuchment (Eds.), Proceedings of the Joint Summer Research Conference on Quantum Graphs and Their Applications, in: Contemporary Mathematics, vol. 415, Snowbird Utah, 2006, pp. 15-33.
2. Baker M., Rumely R. Harmonic analysis on metrized graphs. Canad. J. Math. 2007, 59(2):225-275.
3. Bapat R.B. Resistance matrix of a weighted graph. MATCH Commun. Math. Comput. Chem. 2004, 50:73-82.
4. Bapat R.B. The Laplacian matrix of a graph. Math. Student 1996, 65:214-223.
5. Bapat R.B. Resistance distance in graphs. The Mathematics Student 1999, 68:87-98.
6. Barnett S. Matrices Methods and Applications 1990, Clarendon Press, Oxford.
7. Chinburg T., Rumely R. The capacity pairing. J. Reine Angew. Math. 1993, 434:1-44.
8. Z. Cinkir, The Tau Constant of Metrized Graphs, Thesis at University of Georgia, Athens, GA. 2007.
9. Z. Cinkir, Generalized Foster's identities, Int. J. Quantum Chem., published online March 2010 doi:10.1002/qua.22521.
10. Z. Cinkir, The tau constant of a metrized graph and its behavior under graph operations, Available at (submitted for publication). arxiv:0901.0407v3.
11. Z. Cinkir, The tau constant and the edge connectivity of a metrized graph, Available at (submitted for publication). arxiv:0901.1481v2.
12. I. Gutman, W. Xiao, Bulletin T.CXXIX de l'Académie serbe des sciences et des arts - 2004 Classe des sciences mathématiques et naturelles sciences mathématiques, No. 29, 2004.
13. Klein D.J., Randić M. Resistance distance. J. Math. Chem. 1993, 12:81-95.
14. Merris R. Laplacian matrices of graphs: a survey. Linear Algebra Appl. 1994, 197, 198:143-176.
15. Rao C., Mitra S. Generalized Inverse of Matrices and its Applications 1971, John Wiley and Sons.
16. Summer 2003 Research Experience for Undergraduates (REU) on metrized graphs at the University of Georgia.
17. Rumely R. Capacity Theory on Algebraic Curves. Lecture Notes in Mathematics 1989, vol. 1378. Springer-Verlag, Berlin, Heidelberg, New York.
18. Wolfram Research, Inc., Mathematica Documentation Center, Version 7.0, Champaign, IL, 2008, Available at http://reference.wolfram.com/mathematica/ref/GraphData.html.
19. Wolfram Research, Inc., Mathematica, Version 7.0, Champaign, IL, 2008.
20. Zhang S. Admissible pairing on a curve. Invent. Math. 1993, 112:171-193.
21. Zhang S. Gross-Schoen cycles and dualising sheaves. Invent. Math. 2010, 179:1-73.