References for Computer-Generated Conjectures from

Graph Theoretic and Chemical Databases

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• [C6] Brigham, R.C., and Dutton, R.D., A compilation of relations between graph invariants, Networks, 15 (1985), 73-107.
• [C7] Brigham, R.C., and Dutton, R.D., A compilation of relations between graph invariants. Supplement 1, Networks, 21 (1991) 421-455.
• [C8] Brigham, R.C., Dutton, R.D., and Gomez, F., INGRID: A graph invariant manipulator, J. Symbolic Computation, 7 (1989), 163-177.
• [C9] Brinkmann, G., and Dress, A.W.M., A constructive enumeration of fullerenes, J. Algorithms, 23 (1997), 345-358.
• [C10] Bundy, A., and Colton, S., HR: Automated program formation in pure mathematics, in Processings of IJCAI 1999, to appear.
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• [C12] Caporossi, G., Cvetkovic, D., Gutman, I., and Hansen, P., Variable neighborhood search for extremal graphs. 2. Finding graphs with extremal energy, J. Chemical Information and Computer Sciences, 39 (1999), 984-996.
• [C13] Caporossi, G., Gutman, I., and Hansen, P., Variable neighborhood search for extremal graphs 4: Chemical trees with extremal connectivity index, Computers and Chemistry, 23 (1999), 469-477.
• [C14] Caporossi, G., and Hansen, P., Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system, Discrete Math., 212 (2000), 29-44.
• [C15] Carbonneaux, Y., Laborde, J-M., and Madani, M., Cabri-graphs: A tool for research and teaching in graph theory, Lecture Notes in Computer Science, 1027 (1995), 123-127.
• [C16] Cherlin, G., and Latka, B., A decision problem involving tournaments, DIMACS Technical Report 96-11, 1996.
• [C17] Chung, F., The average distance and the independence number, Journal of Graph Theory, 2 (1988), 229-235.
• [C18] Colton, S., Refactorable numbers -- a machine invention, J. of Integer Sequences, 2 (1999).
• [C19] Cvetkovic, D., Kraus, L.L., and Simic, S.K., Discussing graph theory with a computer, I. Implementation of graph theoretic algorithms, Univ. Beograd Publ. Eletrotehn. Fak. (1981), 100-104.
• [C20] Cvetkovic, D., and Pevac, I., Man-machine theorem proving in graph theory, Artificial Intelligence, 35 (1988), 1-23.
• [C21] Cvetkovic, D., and Simic, S., Graph theoretical results obtained by the support of the expert system ``graph'', Bulletin de l'Academie Serbe des Sciences et des Arts T CVII (1994), 19-41.
• [C22] Cvetkovic, D., Simic, S.,, Caporossi, G., and Hansen, P., Variable neighborhood search for extremal graphs 3: On the largest eigenvalue of color-constrained trees, Linear and Multilinear Algebra, to appear.
• [C23] Dean, N., and Shannon, G.E. (eds.), Computational Support for Discrete Mathematics, DIMACS Series, Vol. 15, American Mathematical Society, Providence, RI, 1994.
• [C24] Epstein, S., On the discovery of mathematical concepts, International J. of Intelligent Systems, 3 (1988), 167-178.
• [C25] Erdos, P., Spencer, J., and Pach, J., On the mean distance between points of a graph, Congressus Numerantium, 63 (1986).
• [C26] Erdos, P., Fajtlowicz, S., and Staton, W., Degree sequences in triangle-free graphs, Discrete Math., 92 (1991), 85-88.
• [C27] Fajtlowicz, S., On conjectures of Graffiti, Discrete Mathematics, 72 (1988), 113-118.
• [C28] Fajtlowicz, S., On conjectures of Graffiti, II, Congressus Numerantium, 60 (1987), 189-197.
• [C29] Fajtlowicz, S., On conjectures of Graffiti, III, Congressus Numerantium, 66 (1988), 23-32.
• [C30] Fajtlowicz, S., On conjectures of Graffiti, IV, Congressus Numerantium, 70 (1990), 231-240.
• [C31] Fajtlowicz, S., On conjectures of Graffiti, V, in Graph Theory, Combinatorics, and Algorithms: Proceedings of the Quadrennial Conference on the Theory and Applications of Graphs, vol. 1, 1995, pp. 367-376.
• [C32] Fowler, P.W., Fullerene graphs with more negative than positive eigenvalues: The exceptions that prove the rule of electron deficiency, J. Chem. Soc. Faraday, 93 (1997), 1-3.
• [C33] Fowler, P.W., Hansen, H., Rogers, K.M., and Fajtlowicz, S., C60Br24 as a chemical illustration of graph theoretical independence, J. of the Chemical Society, Perkin Transactions., 2 (1998), 1531-1533.
• [C34] Griggs, J., and Kleitman, D., Independence and the Havel-Hakimi residue, Discrete Math., 127 (1994), 209-212.
• [C35] Hansen, P., Fowler, P., and Zheng, M. (eds.), Discrete Mathematical Chemistry, DIMACS Series, vol. 51, American Mathematical Society, Providence, RI, 2000.
• [C36] Kotlov, A., and Lovasz, L., The rank and size of graphs, J. of Graph Theory, 23 (1996), 185-189.
• [C37] Laborde, J-M. (ed.), Intelligent Learning Environments, the Case of Geometry, NATO ASI Series, Springer Verlag, Berlin, 1995.
• [C38] Laborde, C., and Laborde, J-M., What about a learning environment where Euclidean concepts are manipulated with a mouse? in A. Dil Sessa, C.M. Hoyles, R. Noss, and L. Edwards (eds.), Computers and Exploratory Learning, NATO ASI Series, Springer Verlag, Berlin, 1995.
• [C39] Larson, C.E., Intelligent machinery and mathematical discovery, http://www.math.uh.edu/~clarson/#mystuff
• [C40] Latka, B., Finitely constained classes of homogeneous directed graphs, J. Symbolic Logic, 59 (1994), 124-139.
• [C41] Lenat, D., Automated theory formation in mathematics, in W. Bledsoe and D. Loveland (eds.), Automated Theorem Proving: After 25 Years, American Mathematical Society, Providence, RI, 1984, pp. 287-314.
• [C42] Mevenkamp, M., Dean, N., and Monma, C., NETPAD user's guide and reference guide, Bellcore, 1990.
• [C43] Shannon, G., Meeden, L., and Friedman, D., SchemeGraphs: An object-oriented environment for manipulating graphs, Indiana University, Bloomington, 1990.
• [C44] Skiena, S., Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Addision-Wesley, Reading, MA, 1990.