Papers on Mathematics

I have authored over 100 research papers on Mathematics. They are listed here by decade:

[1969];[1970s];[1980s];[1990s];[2000s];[2010-]


LINKS TO  DOWNLOADS ARE BEING ADDED

1969

1969

  • Rectangulations. Proc. Cambridge Philos. Soc. 65 (1969) 399-40

1970-1979

1971

  • Intersection matrices for linear graphs. In: Combinatorial Mathematics and its Applications (ed. D.J.A. Welsh), Academic Press (1971) 15-23.
  • Spanning trees of dual graphs. J. Combinatorial Theory (B), 11 (1971) 127-131.
  • Automorphisms of imbedded graphs. J. Combinatorial Theory (B), 11 (1971) 132-138.
  • On trivalent graphs (with D.H. Smith). Bull. London Math. Soc., 3 (1971) 155-158.
  • Classification of complete maps on orientable surfaces. Rendiconti di Matematica (Rome), 4 (1971) 645-655.

1972

  • Recursive families of graphs (with R.M. Damerell and D.A. Sands). J. Combinatorial Theory (B), 12 (1972) 123-131.
  • Cayley maps and symmetrical maps. Proc. Cambridge Philos. Soc., 72 (1972) 381-386.
  • On the symplectic representation of map automorphisms. Bull. London Math. Soc., 4 (1972) 303-306.
  • An edge-colouring problem. Amer. Math. Monthly, 79 (1972) 1018-1020.
  • Pictures. In: Combinatorics, (ed. D.J.A. Welsh and D.R. Woodall), Institute of Mathematics and its Applications (1972) 1-17.

1973

  • Three remarkable graphs. Canadian J. Math., 25 (1973) 397-411.
  • Expansions of the chromatic polynomial. Discrete Mathematics, 6 (1973) 105-113.
  • Perfect codes in graphs. J. Combinatorial Theory (B),15 (1973) 289-296.

1974

 

  •  On the symmetry of line graphs. Utilitas Math. 5 (1974) 113-121.
  • Perfect codes and distance-transitive graphs. In: Combinatorics (eds. V.C Mavron and T. McDonough, LMS Lecture Notes Series No. 13 (1974) 1-8.

1975

  • Designs, factors and codes in graphs. Quart. J. Math. (Oxford), 26 (1975) 113-119.
  • A theorem on planar partitions (with G.H.J. Meredith). Proc. 5th British Combinatorial Conference, (1975) 73-78.
  • Approximations for chromatic polynomials (with G.H.J. Meredith). J. Combinatorial Theory (B), 20 (1976) 5-19.

1976

  • Automorphic graphs and the Krein condition. Geometriae Dedicata, 5 (1976) 117-127.
  • On the duality of interaction models. Math. Proc. Cambridge Philos. Soc., 80 (1976) 429-436.

1977

  • Colouring square lattice graphs. Bull. London Math. Soc., 9 (1977) 54-56.

1978

  • Cluster expansions in graph theory and physics. Quart. J. Math. (Oxford), 29 (1978) 159-174.

1979

  • On the algebra of graph types. In: Graph Theory and Related Topics (ed. J.A. Bondy and U.S.R. Murty), Academic Press (1979) 81-89.
  • Some odd graph theory. Annals of the New York Academy of Sciences, 319 (1979) 71-81.
  • Resonance and reconstruction. In: Surveys on Combinatorics (ed. B. Bollobas), Cambridge University Press (1979) 1-21.

1980-1989

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1980

  • Girth, valency and excess. Linear Algebra and its Applications, 31 (1980) 55-59.
  • Graphs with even girth and small excess (with T. Ito). Math. Proc. Cambridge Philos. Soc., 88 (1980) 1-10.
  • A trivalent graph with girth 9 and 58 vertices (with M. Hoare). Discrete Math., 30 (1980) 299-301. [DownloadM1980c]

1981

  • Aspects of symmetry in graphs. In: Algebraic Methods in Graph Theory (ed. L. Lovász and V. Sos), North-Holland (1981) 27-35.
  • Covering biplanes. In: Theory and Applications of Graphs (ed. G. Chartrand et al.), Wiley (1981) 73-82.
  • Covering graphs and symmetric designs (with T. Ito). In: Finite Geometries and Designs, (ed. P.J. Cameron et al.), Cambridge University Press (1981) 40-51.

1982

  • Excess in vertex-transitive graphs. Bull. London Math. Soc., 14 (1982) 52-54.
  • Distance-regular graphs with diameter 3. Ann. Discrete Math., 15 (1982) 69-80.
  • Constructing 5-arc-transitive cubic graphs. J. London Math. Soc. (2), 26 (1982) 193-200.
  • A new 5-arc-transitive cubic graph. J. Graph Theory, 6 (1982) 447-451.

1983

  • The sextet construction for cubic graphs (with M.J. Hoare). Combinatorica, 3 (1983) 153-165.

1984

  • Presentations for cubic graphs. In: Computational Group Theory (ed. M.D. Atkinson). Academic Press (1984) 57-63.
  • Homological coverings of graphs. J. London Math. Soc. (2), 30 (1984) 1-14.
  • Rotations and graphs of large girth (with J. Shawe-Taylor). In: Geometrical Combinatorics (ed. F.C. Holroyd and R.J. Wilson), Pitman (1984) 1-9.

1985

  • Infinite covers of cages (with S.K. Burford). Europ. J. Combinatorics, 6 (1985) 7-12.

1986

  • Cubic distance-regular graphs (with A.G. Boshier and J. Shawe-Taylor) J. London Math. Soc. (2), 33 (1986) 385-394.

1988

  • The spectral radius of infinite graphs (with B. Mohar and J. Shawe-Taylor) Bull. London Math. Soc., 20 (1988) 116-120.
  • Girth and residual finiteness. Combinatorica, 8 (1988) 307-312.
  • Graphs with large girth. Ars Combinatoria, 25-C (1988) 73-80.

1989

  • Cubic graphs with large girth. Annals of the New York Academy of Sciences, 555 (1989) 56-62.
  • Confluence of some presentations associated with graphs. Discrete Math., 75 (1989) 56-62.
  • A proof of Serre's theorem. Discrete Math., 78 (1989) 55-57.
  • The growth rate of the harmonious chromatic number (with D. Beane and B.J. Wilson). J. Graph Theory, 13 (1989) 291-299.

1990-1999

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1990

  • Note on the girth of Ramanujan graphs (with A.G. Boshier). J. Combinatorial Theory (B), 49 (1990) 190-194.
  • Some heuristics for graph colouring. In: Graph Colourings (ed. R. Nelson and R.J. Wilson), Pitman Research Notes in Mathematics 218, Longmans (1990) 87-96.
  • The learnability of formal concepts (with M.H.G. Anthony and J. Shawe-Taylor). Proceedings of the Third Annual Workshop on Computational Learning Theory (COLT 1990), M.A. Fulk (ed.), Morgan-Kaufmann, San Mateo Ca. (1990) 246-257.

1992

  • Learning algorithms: theory and practice. In: Neural Network Applications (ed. J.G. Taylor), Springer (1992) 1-11.
  • Theoretical and practical studies of a competitive learning process (with G.R. Brightwell and D. Tsoubelis). Network 3 (1992) 285-301.
  • A framework for cumulative learning. Mathematics Preprint Series, LSE-MPS-27, London School of Economics, 1992.

1993

  • Bounding sample size with the Vapnik-Chervonenkis dimension (with M.H.G. Anthony and J. Shawe-Taylor). Discrete Applied Mathematics 42 (1993) 65-73.
  • The mean chromatic number of paths and cycles (with M.H.G. Anthony). Discrete Mathematics 120 (1993) 227-231.
  • Computational learning theory for artificial neural networks (with M.H.G. Anthony). In: Mathematical Approaches to Neural Networks (ed. J.G. Taylor), North-Holland (1993) 25-62.
  • Discrete Mathematics in Finance: Two Applications, Mathematics Preprint Series LSE-MPS- 49, London School of Economics, 1993.
  • Potential theory on distance-regular graphs. Combinatorics, Probability and Computing 2 (1993) 243-255.

1994

  • Combinatorics and connectionism. Discrete Math. 124 (1994) 19-36.
  • Exchange rate networks and mechanisms. Mathematics Preprint Series, LSE-MPS-64, London School of Economics, December 1993, revised May 1994.
  • PAC learning and artificial neural networks (with M.H.G. Anthony). In: The Handbook of Brain Theory and Neural Networks, (ed. M.A. Arbib), Bradford/MIT Press (1994).
  • Exchange rates and the matrix-tree theorem. Theoretical Economics Discussion Papers TE/94/273, London School of Economics, 1994.
  • How to compute the spectral density of a lattice and its quotients. Mathematics Preprint Series, LSE-MPS-74, London School of Economics, October 1994.

1995

  • The spectral density of covering lattices. Mathematics Preprint Series, LSE-MPS-78, London School of Economics, January 1995.
  • A computational learning theory view of economic forecasting with neural nets (with M.H.G. Anthony). In: Neural Networks in the Capital Markets (ed.A.Refenes), Wiley (1995) 77-98.
  • Algorithms for learning and coloring. In: Graph Theory, Combinatorics and Applications, (ed. Y. Alavi and A. Schwenk), Wiley (1995) 63-70.
  • The potential of potential theory. LSE Mathematics Preprint Series, LSE-MPS-91, September 1995.

1996

  • Chip-firing on distance-regular graphs. CDAM Research Report Series, LSE-CDAM-96-11, June 1996.

1997

  • International Finance. In: Graph Connections (ed. L.W. Beineke and R.J. Wilson), Oxford University Press (1997) 261-279.
  • Chip-firing and the chromatic polynomial (with P. Winkler). CDAM Research Report Series, LSE-CDAM-97-03, February 1997.
  • Integer programming techniques for the frequency assignment problem. CDAM Research Report Series, LSE-CDAM-97-06, April 1997.
  • Algebraic potential theory on graphs. Bull. London Math. Soc. 29 (1997) 641-682

1998

  • Constructions for cubic graphs with large girth. Electronic Journal of Combinatorics 5 (1998) A1. PDF.
  • Optimising the signal-to-noise ratio (with D Fon der Flaass). CDAM Research Report Series, LSE-CDAM-98-16, August 1998.

1999

  • Chip-firing and the critical group of a graph. J. Algebraic Combinatorics, 9 (1999) 25-45.
  • The Tutte polynomial as a growth function. Journal of Algebraic Combinatorics 10 (1999) 115-133.
  • The chromatic polynomial of the 3 x n toroidal square lattice. CDAM Research Report Series, LSE-CDAM 99-05, June 1999.
  • T=0 partition functions for Potts antiferromagnets on square lattice strips with (twisted) periodic boundary conditions (with R.Shrock). J.Phys. A. 32 (1999) L489-L493.

2000-2009

2000

  • A matrix method for chromatic polynomials – II. CDAM Research Report Series, LSE-CDAM 2000-04, April 2000.
  • (NB and P.Reinfeld). The chromatic roots of generalised dodecahedra. CDAM Research Report Series, LSE-CDAM 2000-07, June 2000.

2001

  • Equimodular curves for reducible matrices CDAM Research Report Series, LSE-CDAM 2001-01, January 2001. PDF.
  • A matrix method for chromatic polynomials. J. Combinatorial Theory (B), 82 (2001) 19-29.

2002

  • Chromatic polynomials for twisted bracelets. Bull. London Math. Soc. 34 (2002) 129-139.
  • Chromatic polynomials and representations of the symmetric group. Linear Algebra and its Applications 356 (2002) 3-26.
  • Equimodular curves. Discrete Mathematics 259 (2002) 37-57.

2004

  • Algebraic methods for chromatic polynomials (with M H Klin and P Reinfeld). Europ. J. Combinatorics 25 (2004) 147-160.
  • Specht modules and chromatic polynomials. J. Combinatorial Theory (B) 92 (2004) 359 - 377.   [Download M2004b]

2005

  • Chromatic polynomials of some families of graphs I: Theorems and Conjectures. CDAM Research Report Series, LSE-CDAM 2005-09, May 2005. PDF.

2007

  • The critical group from a cryptographic perspective. Bull. London Math. Soc. , 39 (2007) 829-836.    [Download  M2007]

2008

  • Chromatic Roots of the Quartic Mobius Ladders CDAM Research Report LSE-CDAM 2008-05, May 2008. PDF.
  • A Matrix Method for Flow Polynomials. CDAM Research Report LSE-CDAM 2008-08, June 2008. PDF.

2009

  • Tutte Polynomials of Bracelets. CDAM Research Report LSE-CDAM-2009-01, January 2009. PDF.
  • Strongly Regular Graphs with No Triangles. Research Report, September 2009. arXiv:0911.2160v1 PDF.
  • Families of Parameters for SRNT Graphs. Research Report, October 2009. arXiv:0911.2455v1 PDF

2010-

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2010

  • Tutte Polynomials of Bracelets. J. Algebraic Combinatorics 32 (2010) 389-398.
  • The Second Subconstituent of some Strongly Regular Graphs. Research Report, February 2010. arXiv:1003.0175v1 PDF.

2011

  • Some Properties of Strongly Regular Graphs. Research Report, May 2011. arXiv:1106.0889v1 PDF.

2015

  • (NB and F. de Ruiter) Applications of Integer Programming Methods to Cages. Electronic J. Combinatorics 22(4) (2015) #P4.35. [Download M2015]

2017

  • Chromatic polynomials and toroidal graphs. Australasian Journal of Mathematics 67(2) (2017) 235-242. [Download M2017]