Abstract
Graph designs for all graphs with six vertices and eight edges are discussed. The existence of these graph designs are completely solved except in two possible cases of order 32.
Similar content being viewed by others
References
Alspach, B., Gavlas, H. Cycle decompositions of K n and K n −I. Journal of Combinatorial Theory (Series B), 21:146–155 (2000)
Bermond, J.C., Huang, C., Rosa, A., Sotteau, D. Decomposition of complete graphs into isomorphic subgraphs with five vertices. Ars Combinatoria, 10:211–254 (1980)
Bermond, J.C., Schönheim, J. G-decomposition of K n , where G has four vertices or less. Discrete Math., 19:113–120 (1977)
Blinco, A. On diagonal cycle systems. Australasian Journal of Combinatorics, 24:221–230 (2001)
Bosak, J. Decompositions of graphs. Kluwer Academic Publishers, Boston, 1990
Chang, Y. The spectra for two classes of graph designs. Ars Combinatoria, 65:237–243 (2002)
Colbourn, C.J., Dinitz, J.H.(eds.) The CRC handbook of combinatorial designs. CRC Press, Boca Raton, 1996
Ge, Gennian. Existence of holey LSSOM of type 2n with application to G7-packing of Kv. J. Statist. Plan. Infer., 94:211–218 (2001)
Harary, F. Graph theory. Addison-Wesley, Reading, 1969
Heinrich, K. Path-decomposition. Le Mathematics (Catania) XLVII:241–258 (1992)
Kang, Q.D., Du, Y.K., Tian, Z.H. Decompositions of λKv into some graph with six vertices and seven edges. Journal of Statistical Planning and Inference, available online 2 December 2004.
Kang, Q.D., Du, Y.K., Tian, Z.H. Decomposition of complete graph into isomorphic subgraphs with six vertices and seven edges. to appear in Ars Combinatoria. (accepted on March, 2005)
Kang, Q.D., Zhang, Y.F., Zuo, H.J. λ- packings and λ-coverings by k-circuits with one chord. Discrete Mathematics, 279:287–315 (2004)
Kang, Q.D., Zuo, H.J., Zhang, Y.F. Decompositions of λK v into k-circuits with one chord. Australasian Journal of Combinatorics, 30:229–246 (2004)
Kang, Q.D., Wang, Z.Q. Optimal packings and coverings of λKv with graph K 5 − P 5. Bulletin of the Institute of Combinatorics and its Applications, 41:22–41 (2004)
Kang, Q.D., Wang, Zhiqin. Maximum K 2,3-packing and minimum K 2,3-covering designs of λK v . Journal of Mathematical Research and Exposition, 25:1–16 (2005)
Kotzig, A. Decomposition of complete graphs into isomorphic cubes. J. Combin. Theory (Series B), 31:292–296 (1981)
Rodger, C.A. Graph-decompositions. Le Mathematics (Catania) XLV:119–140 (1990)
Rosa, A. On certain valuations of the vertices of a graph, Theory of Graphs, (Internat. Symmposium, Rome, July 1966), Gordon and Breach, N.Y. and Dunod Paris, 349–355 1967
Yin, J., Gong, B. Existence of G-designs with |V (G)| = 6, In:W.D. Wallis et al.(eds). Combinatorial designs and applications, Marcel Dekker, New York, 201–218 1990
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Natural Science Foundation of China (No.10371031) and Natural Science Foundation of Hebei (No.103146).
Rights and permissions
About this article
Cite this article
Kang, Qd., Yuan, Ld. & Liu, Sx. Graph Designs for all Graphs with Six Vertices and Eight Edges. Acta Mathematicae Applicatae Sinica, English Series 21, 469–484 (2005). https://doi.org/10.1007/s10255-005-0254-7
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10255-005-0254-7