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Combinatorics

Graph Theory

05Cxx

[1] David Abelson, Seok-Hee Hong, and Donald E. Taylor. A group-theoretic method for drawing graphs symmetrically. In Graph Drawing, volume 2528 of Lecture Notes in Comput. Sci., pages 86–97. Springer, Berlin, 2002.
[2] Eiichi Bannai, Osamu Shimabukuro, and Hajime Tanaka. Finite analogues of non-Euclidean spaces and Ramanujan graphs. European J. Combin., 25(2):243–259, 2004.
[3] Wayne Barrett, Jason Grout, and Raphael Loewy. The minimum rank problem over the finite field of order 2: minimum rank 3. arXiv:math.CO/0612331, 38 pages, 2006.
[4] C. Bates, D. Bundy, S. Perkins, and P. Rowley. Commuting involution graphs for symmetric groups. J. Algebra, 266(1):133–153, 2003.
[5] Norman Biggs. Constructions for cubic graphs with large girth. Electron. J. Combin., 5:Article 1, 25 pp. (electronic), 1998.
[6] John M. Boyer and Wendy J. Myrvold. On the cutting edge: Simplified O(n) planarity by edge addition. J. Graph Algorithms Appl., 8(3):241–273 (electronic), 2004.
[7] John Bray, Christopher Parker, and Peter Rowley. Cayley type graphs and cubic graphs of large girth. Discrete Math., 214(1-3):113–121, 2000.
[8] Marston Conder. Constructing symmetric graphs. Theta, 3:11–16, 1989.
[9] Marston Conder. Group actions on graphs, maps and surfaces with maximum symmetry. In Groups St. Andrews 2001 in Oxford. Vol. I, volume 304 of London Math. Soc. Lecture Note Ser., pages 63–91. Cambridge Univ. Press, Cambridge, 2003.
[10] Marston Conder and Peter Dobcsányi. Determination of all regular maps of small genus. J. Combin. Theory Ser. B, 81(2):224–242, 2001.
[11] Marston Conder and Peter Dobcsányi. Trivalent symmetric graphs on up to 768 vertices. J. Combin. Math. Combin. Comput., 40:41–63, 2002.
[12] Marston Conder and Brent Everitt. Regular maps on non-orientable surfaces. Geom. Dedicata, 56(2):209–219, 1995.
[13] Marston Conder, Robert Jajcay, and Tom Tucker. Regular Cayley maps for finite abelian groups. J. Algebraic Comb., 25:2259–283, 2007.
[14] Marston Conder and Cai Heng Li. On isomorphisms of finite Cayley graphs. European J. Combin., 19(8):911–919, 1998.
[15] Marston Conder and Peter Lorimer. Automorphism groups of symmetric graphs of valency 3. J. Combin. Theory Ser. B, 47(1):60–72, 1989.
[16] Marston Conder, Peter Lorimer, and Cheryl Praeger. Constructions for arc-transitive digraphs. J. Austral. Math. Soc. Ser. A, 59(1):61–80, 1995.
[17] Marston Conder, Aleksander Malnič, Dragan Marušič, Tomaž Pisanski, and Primož Potočnik. The edge-transitive but not vertex-transitive cubic graph on 112 vertices. J. Graph Theory, 50(1):25–42, 2005.
[18] Marston Conder, Aleksander Malnič, Dragan Marušič, and Primož Potočnik. A census of semisymmetric cubic graphs on up to 768 vertices. J. Algebraic Combin., 23(3):255–294, 2006.
[19] Marston Conder and Dragan Marušič. A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer. J. Combin. Theory Ser. B, 88(1):67–76, 2003.
[20] Marston Conder, Margaret Morton, and Cheryl E. Praeger. Partition graphs for finite symmetric groups. J. Graph Theory, 25(2):107–117, 1997.
[21] Marston Conder, Margaret Morton, and Cheryl E. Praeger. Two-arc closed subsets of graphs. J. Graph Theory, 42(4):350–364, 2003.
[22] Marston Conder and Roman Nedela. Symmetric cubic graphs of small girth. J. Combin. Theory Ser. B, 97:757–768, 2007.
[23] Marston Conder and Steve Wilson. Inner reflectors and non-orientable regular maps. Discrete Math., 307(3-5):367–372, 2007.
[24] Marston D. E. Conder and Cameron G. Walker. The infinitude of 7-arc-transitive graphs. J. Algebra, 208(2):619–629, 1998.
[25] Italo J. Dejter. On Clique Turan graph-homogeneity. arXiv:0704.2146, 20 pages, 2007.
[26] Italo J. Dejter. On (K4, K2, 2, 2)-ultrahomogeneity. arXiv:0704.1493, 16 pages, 2007.
[27] Xin Gui Fang, George Havas, and Cheryl E. Praeger. On the automorphism groups of quasiprimitive almost simple graphs. J. Algebra, 222(1):271–283, 1999.
[28] Xin Gui Fang, George Havas, and Jie Wang. Automorphism groups of certain non-quasiprimitive almost simple graphs. In Groups St. Andrews 1997 in Bath, I, volume 260 of London Math. Soc. Lecture Note Ser., pages 267–274. Cambridge Univ. Press, Cambridge, 1999.
[29] Yan-Quan Feng, Klavdija Kutnar, Aleksander Malnič, and Dragan Marušič. On 2-fold covers of graphs. arXiv:math.CO/0701722, 18 pages, 2007.
[30] Louis Ferré and Bertrand Jouve. Vertex partitioning of a class of digraphs. Math. Sci. Hum., (158):59–77, 2002.
[31] Michael Giudici, Cai Heng Li, Primož Potočnik, and Cheryl E. Praeger. Homogeneous factorisations of complete multipartite graphs. Discrete Math., 307(3-5):415–431, 2007.
[32] Jason Grout. Ultraconnected and Critical Graphs. Master of science, Brigham Young University, 2003.
[33] Paul R. Hafner. Large Cayley graphs and digraphs with small degree and diameter. In Computational Algebra and Number Theory (Sydney, 1992), volume 325 of Math. Appl., pages 291–302. Kluwer Acad. Publ., Dordrecht, 1995.
[34] Paul R. Hafner. Geometric realisation of the graphs of McKay-Miller-širáň. J. Combin. Theory Ser. B, 90(2):223–232, 2004.
[35] Paul R. Hafner. On the graphs of Hoffman-Singleton and Higman-Sims. Electron. J. Combin., 11(1):Research Paper 77, 33 pp. (electronic), 2004.
[36] Robert E. Jamison and Gretchen L. Matthews. Distance k colorings of Hamming graphs. Preprint, 10 pages, 2006.
[37] Peter Keevash and Benny Sudakov. Packing triangles in a graph and its complement. J. Graph Theory, 47(3):203–216, 2004.
[38] Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, and Štefko Miklavič. Distance-balanced graphs: Symmetry conditions. Discrete Math., 306(16):1881–1894, 2006.
[39] Klavdija Kutnar and Dragan Marušič. Hamiltonicity of vertex-transitive graphs of order 4p. arXiv:math.CO/0606585, 17 pages, 2006.
[40] Klavdija Kutnar and Primož Šparl. Hamilton paths and cycles in vertex-transitive graphs of order 6p. arXiv:math/0702182, 21 pages, 2007.
[41] Felix Lazebnik and Raymond Viglione. An infinite series of regular edge- but not vertex-transitive graphs. J. Graph Theory, 41(4):249–258, 2002.
[42] Paulette Lieby. Colouring planar graphs. In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 315–330. Springer, Berlin, 2006.
[43] Tian Khoon Lim. Edge-transitive homogeneous factorisations of complete graphs. arXiv:math.CO/0605253, 130 pages, 2004.
[44] Tian Khoon Lim. Arc-transitive homogeneous factorizations and affine planes. J. Combin. Des., 14(4):290–300, 2006.
[45] Tian Khoon Lim and Cheryl E. Praeger. On generalised Paley graphs and their automorphism groups. arXiv:math/0605252, 20 pages, 2006.
[46] Marko Lovrečič Saražin, Walter Pacco, and Andrea Previtali. Generalizing the generalized Petersen graphs. Discrete Math., 307(3-5):534–543, 2007.
[47] Aleksander Malnič, Dragan Marušič, Štefko Miklavič, and Primož Potočnik. Semisymmetric elementary abelian covers of the Möbius-Kantor graph. arXiv:math.CO/0510383 v1, 22 pages, 2005.
[48] Aleksander Malnič, Dragan Marušič, and Primož Potočnik. Elementary abelian covers of graphs. J. Algebraic Combin., 20(1):71–97, 2004.
[49] Aleksander Malnič, Dragan Marušič, and Primož Potočnik. On cubic graphs admitting an edge-transitive solvable group. J. Algebraic Combin., 20(1):99–113, 2004.
[50] Aleksander Malnič, Dragan Marušič, and Primož Šparl. On strongly regular bicirculants. European J. Combin., 28(3):891–900, 2007.
[51] Aleksander Malnič and Primož Potočnik. Invariant subspaces, duality, and covers of the Petersen graph. European J. Combin., 27(6):971–989, 2006.
[52] Dragan Marušič. On 2-arc-transitivity of Cayley graphs. J. Combin. Theory Ser. B, 87(1):162–196, 2003.
[53] Dragan Marušič and Primož Potočnik. Bridging semisymmetric and half-arc-transitive actions on graphs. European J. Combin., 23(6):719–732, 2002.
[54] Margaret Morton. A note on arc-transitive circulants. Bull. Inst. Combin. Appl., 23:63–68, 1998.
[55] Alen Orbanić. Parallel-product decomposition of edge-transitive maps. arXiv:math.CO/0510428, 30 pages, 2005.
[56] Michael E. O'Sullivan. Algebraic construction of sparse matrices with large girth. IEEE Trans. Inform. Theory, 52(2):718–727, 2006.
[57] C. W. Parker. Semisymmetric cubic graphs of twice odd order. European J. Combin., 28(2):572–591, 2007.
[58] Christopher Parker and Peter Rowley. Ω-covers of graphs. Bull. London Math. Soc., 32(6):658–662, 2000.
[59] Christopher Parker and Peter Rowley. Subgroup-chain graphs. Graphs Combin., 19(4):537–545, 2003.
[60] Manley Perkel and Cheryl E. Praeger. Polygonal graphs: New families and an approach to their analysis. In Proceedings of the Twenty-eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1997), volume 124, pages 161–173, 1997.
[61] Manley Perkel, Cheryl E. Praeger, and Richard Weiss. On narrow hexagonal graphs with a 3-homogeneous suborbit. J. Algebraic Combin., 13(3):257–273, 2001.
[62] Cheryl E. Praeger and Leonard H. Soicher. Low Rank Representations and Graphs for Sporadic Groups, volume 8 of Australian Mathematical Society Lecture Series. Cambridge University Press, Cambridge, 1997.
[63] Nicolas M. Thiéry. Algebraic invariants of graphs; A study based on computer exploration. SIGSAM Bulletin, 34(3):9–20, 2000.
[64] Libero Verardi. Matrices, graphs and equivalence relations. Ann. Mat. Pura Appl. (4), 180(4):413–428, 2002.
[65] Yan Wang, Xin Gui Fang, and D. F. Hsu. On the edge-forwarding indices of Frobenius graphs. Acta Math. Sin. (Engl. Ser.), 22(6):1735–1744, 2006.
[66] Doug Wiedemann and Michael Zieve. Equivalence of sparse circulants: The bipartite Adam problem. arXiv:0706.1567, 20 pages, 2007.

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