An application of p -factorization methods to symmetric graphs

title: On a theorem of Goldschmidt

title: A characterization of the group Co 3 as a transitive extension of HS

title: Presentations for (G,s)-transitive graphs of small valency
abstract: Given a group G , a subgroup H and an element a ∈ G , we define Γ( G, H, a ) to be the graph on the set of left-cosets of H in G , where two left-cosets g 1 H and g 2 H are adjacent whenever . We will consider this construction only in the case that The first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ( G, H, a ) is an undirected graph) and the second assures that Γ( G, H, a ) is connected.

title: The nonexistence of 8-transitive graphs
abstract: We prove that the inequalitys≦7 holds for finites-transitive graphs assuming that the list of known 2-transitive permutation groups is complete.

title: Distance-transitive graphs and generalized polygons
abstract: On etablit un theoreme sur un graphe Γ connexe, regulier de valence k≥3, circonference finie g, avec s≥4. Γ est (G,s)-transitif pour G≤aut(Γ) tel que G(x) est fini pour chaque sommet x

title: Algorithm 546: SOLVEBLOK [F4]
abstract: Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for dtrect commercial advantage, the ACM copymght notice and the title of the pubhcation and its date appear, and notme is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to repubhsh, requires a fee and/or specific permission.

title: The application of implicit Runge-Kutta and collection methods to boundary-value problems
abstract: The solution of a nonlinear system of first order differential equations with nonlinear boundary conditions by implicit Runge-Kutta methods based on interpolatory quadrature formulae is examined. An equivalence between implicit Runge-Kutta and collocation schemes is established. It is shown that the difference equations obtained have a unique solution in a neighbourhood of an isolated solution of the continuous problem, that this solution can be computed by Newton iteration and that it converges to the isolated solution. The order of convergence is equal to the degree of precision of the related quadra- ture formula plus one. The efficient implementation of the methods is discussed and numerical examples are given. 1.  We investigate the application of certain implicit Runge- Kutta methods (cf. Butcher (2)) to the numerical solution of nonlinear boundary- value problems of the form

title: The convergence of shooting methods
abstract: Shooting methods for nonlinear boundary value problems are examined. It is shown that the methods converge whenever the problem is well posed in the sense that the solution to be computed is isolated.

title: On the Approximation of Fixed Points of Nonlinear Compact Operators
abstract: Certain methods for the approximate solution of $x - Kx = 0$, where K is a compact operator, lead to a family of operator equations $x - K_n x = 0$, $n \geqq 1$, where $K_n $,$n \geqq 1$, are collectively compact and converge pointwise to K. In this paper a new and simplified proof of the existence and uniqueness of a solution of $x - K_n x = 0$ in a neighborhood of an isolated solution of $x - Kx = 0$ is given.

title: Symmetric graphs with projective subconstituents
abstract: Let P be an undirected graph and G a subgroup of aut(r) acting transitively on the vertex set of P. Let x be an arbitrary vertex of P. We denote by P(x) the set of vertices adjacent to x and by G(x)F(x) the permutation group induced by the stabilizer G (x) of x in G on P(x); G (x)r(X) is called the subconstituent of the pair (P, G). For each i E N let Gi(x) = {a E G(x)Ia E G(y) if a (x, y) 1 then s 3. In , it was shown that s 3. We prove the following partial result: