Algebraic potential theory on graphs

Bulletin of the London Mathematical Society

Volumn 29, Issue 6, 1997, Pages 641-682

  Biggs, Norman ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001502671     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024609397003305     Document Type: Article

References (32)

1. D. ALDOUS, 'An introduction to covering problems for random walks on graphs', J. Theoret. Probab. 2 (1989) 87-120.
2. R. BACHER, P. DE LA HARPE and T. NAGNIBEDA, 'The lattice of integral flows and the lattice of integral coboundaries on a finite graph', Bull. Soc. Math. France, to appear.
3. K. A. BERMAN, 'A graph-theoretical approach to the handicap ranking of tournaments and paired comparisons', SIAM J. Algebraic Discrete Methods 1 (1980) 359-361.
4. K. A. BERMAN, 'Balanced vertex-weightings and arborescences', J. Combin. Theory Ser. B 42 (1987) 274-301.
5. N. L. BIGGS, Algebraic graph theory (Cambridge University Press, 2nd edn, 1993).
6. N. L. BIGGS, 'Potential theory on distance-regular graphs', Combin. Probab. Comput. 2 (1993) 243-255.
7. N. L. BIGGS, 'International finance', Graph connections (ed. L. W. Beineke and R. J. Wilson, Oxford University Press, 1997) 261-279.
8. N. L. BIGGS, 'Chip firing and the critical group of a graph', J. Algebraic Combin., to appear.
9. A. BJÖRNER and L. LOVÁSZ, 'Chip-firing games on directed graphs', J. Algebraic Combin. 1 (1992) 305-328.
10. A. BJÖRNER, L. LOVÁSZ and P. SHOR, 'Chip-firing games on graphs', European J. Combin. 12 (1991) 283-291.
11. B. BOLLOBÁS and G. BRIGHTWELL, 'Random walks and electrical resistances in products of graphs', Discrete Appl. Math. 73 (1997) 69-79.
12. R. L. BROOKS, C. A. B. SMITH, A. H. STONE and W. T. TUTTE, 'Dissection of a rectangle into squares', Duke Math. J. 7 (1940) 312-340.
13. A. E. BROUWER, A. M. COHEN and A. NEUMAIER, Distance-regular graphs (Springer, Berlin, 1989).
14. A. E. BROUWER and C. A. VAN EIJL, 'On the p-rank of the adjacency matrices of strongly-regular graphs', J. Algebraic Combin. 1 (1992) 329-346.
15. W-K. CHEN, 'On vector spaces associated with a graph', SIAM J. Appl. Math. 20 (1971) 526-529.
16. W-K. CHEN, Applied graph theory: graphs and electrical networks (North-Holland, New York, 1976).
17. D. DHAR, 'Self-organised critical state of sandpile automaton models', Phys. Rev. Lett. 64 (1990) 1613-1618.
18. P. G. DOYLE and J. L. SNELL, Random walks and electrical networks (Math. Assoc. America, Washington, DC, 1984).
19. R. M. FOSTER, 'The average impedance of an electrical network', Reissner Anniversary Volume -Contributions to applied mechanics (J. W. Edwards, Ann Arbor, MI, 1949) 333-340.
20. R. M. FOSTER, 'An extension of a network theorem', IRE Trans. Circuit Theory CT-8 (1961) 75-76.
21. A. GABRIELOV, 'Abelian avalanches and Tutte polynomials', Phys. A 195 (1993) 253-274.
22. G. KIRCHHOFF, 'Uber die Auflösung der Gleichungen, auf welche man bei der Untersuchungen der linearen Vertheilung galvanischer Ströme geführt wird,' Ann. Phys. Chem. 72 (1847) 497-508.
23. J. C. LAGARIAS, 'Point lattices', Handbook of combinatorics, Vol. I (ed. R. Graham, M. Grötschel and L. Lovász, Elsevier, Amsterdam, 1995) 923-945.
24. L. LOVÁSZ and P. WINKLER, 'Mixing of random walks and other diffusions on a graph', Surveys in combinatorics 1995 (ed. P. Rowlinson, Cambridge University Press, 1995) 119-154.
25. 12', J. Algebra 156 (1993) 362-369.
26. J. W. MOON and N. J. PULLMAN, 'On generalised tournament matrices', SIAM Rev. 12 (1970) 384-399.
27. A. NERODE and H. SHANK, 'An algebraic proof of Kirchhoff's network theorem', Amer. Math. Monthly 68 (1961) 244-247.
28. H. SHANK, 'Graph property recognition machines', Math. Systems Theory 5 (1971) 45-49.
29. P. TETALI, 'Random walks and the effective resistance of networks', J. Theoret. Probab. 4 (1991) 101-109.
30. P. TETALI, 'An extension of Foster's network theorem', Combin. Probab. Comput. 3 (1994) 421-427.
31. C. THOMASSEN, 'Resistances and currents in infinite electrical networks', J. Combin. Theory Ser. B 49 (1990) 87-102.
32. W. T. TUTTE, Graph theory (Addison-Wesley, Reading, MA, 1984).