4,785 research outputs found

    In search of an appropriate abstraction level for motif annotations

    Get PDF
    In: Proceedings of the 2012 Workshop on Computational Models of Narrative, (pp. 22-28).

    On 2-switches and isomorphism classes

    Get PDF
    A 2-switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degree sequence may be changed into each other via sequences of 2-switches. We show that if a 2-switch changes the isomorphism class of a graph, then it must take place in one of four configurations. We also present a sufficient condition for a 2-switch to change the isomorphism class of a graph. As consequences, we give a new characterization of matrogenic graphs and determine the largest hereditary graph family whose members are all the unique realizations (up to isomorphism) of their respective degree sequences.Comment: 11 pages, 6 figure

    On rainbow tetrahedra in Cayley graphs

    Full text link
    Let Γn\Gamma_n be the complete undirected Cayley graph of the odd cyclic group ZnZ_n. Connected graphs whose vertices are rainbow tetrahedra in Γn\Gamma_n are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs GG of largest degree 6, asymptotic diameter ∣V(G)∣1/3|V(G)|^{1/3} and almost all vertices with degree: {\bf(a)} 6 in GG; {\bf(b)} 4 in exactly six connected subgraphs of the (3,6,3,6)(3,6,3,6)-semi-regular tessellation; and {\bf(c)} 3 in exactly four connected subgraphs of the {6,3}\{6,3\}-regular hexagonal tessellation. These vertices have as closed neighborhoods the union (in a fixed way) of closed neighborhoods in the ten respective resulting tessellations. Generalizing asymptotic results are discussed as well.Comment: 21 pages, 7 figure

    The random graph

    Full text link
    Erd\H{o}s and R\'{e}nyi showed the paradoxical result that there is a unique (and highly symmetric) countably infinite random graph. This graph, and its automorphism group, form the subject of the present survey.Comment: Revised chapter for new edition of book "The Mathematics of Paul Erd\H{o}s
    • …
    corecore