Journal of Combinatorial Designs最新文献

It is shown that the flag-transitive, point-primitive automorphism groups of 2-$��\left(�\; ��v�\; �,�\; �k�\; �,�\; �\lambda ��\; �\right)�$ designs with $��\lambda �$ prime must be of affine type or almost simple type.

A set of edges $��\Gamma �$ of a graph $��G�$ is an edge dominating set if every edge of $��G�$ intersects at least one edge of $��\Gamma �$, and the edge domination number $��{\gamma }_e�\; ��\left(�\; �G�\; �\right)��$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study $��{\gamma }_e�\; ��\left(�\; �G�\; �\right)��$ for graphs $��G�$ which are the incidence graph of some incidence structure $��D�$, with an emphasis on the case when $��D�$ is a symmetric design. In particular, we show in this latter case that determining $�$

Let $�\; ��D�\; �=�\; ��\left(�\; ��P�\; �,�\; �ℬ��\; �\right)��$ be a nontrivial symmetric $�\; ���\left(�\; ��v�\; �,�\; �k�\; �,�\; �\lambda ��\; �\right)��$-design with $�\; ��\lambda �\; �\le �\; �100�$, and let $�\; ��G�$ be a flag-transitive automorphism group of $�\; ��D�$. In this paper, we show that if $�\; ��G�$ is quasiprimitive on $�\; ��P�$, then $�\; ��G�$ is of holomorph affine or almost simple type. Moreover, if $�\; ��G�$ is imprimitive on $�\; ��P�$, then $�\; ��G�$ is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.

In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of equal odd length. We prove that the complete symmetric digraph on $��2�m�$ vertices, denoted $��K_{�2�m�}^{*}�$, admits a resolvable decomposition into directed cycles of odd length $��m�$. This completely settles the directed Oberwolfach problem with tables of uniform length.

Let $��G�$ be a simple graph and $��\lambda �\; ��\left(�\; �G�\; �\right)��$ the spectral radius of $��G�$. For $��k�\; �\ge �\; �2�$, a $��k�$-edge decomposition $��\left(�\; ��H_1�\; �,�\; �\dots �\; �,�\; �H_k��\; �\right)�$ is $��k�$ spanning subgraphs such that their edge sets form a $��k�$-partition of the edge set of $��G�$. In this paper, we obtain some sharp lower and upper bounds for $��\lambda �\; ��(�\; �$

Xu characterized rank 4 self-dual association schemes inducing three partial geometric designs by their character tables. We construct such association schemes as Schur rings over Abelian 2-groups.

Let $��S�$ be a finite proper partial geometry pg$���\left(��s�\; �,�\; �t�\; �,�\; �\alpha ��\; �\right)��$ not isomorphic to the van Lint–Schrijver partial geometry pg$���\left(��5�\; �,�\; �5�\; �,�\; �2��\; �\right)��$ and let $��G�$ be a group of automorphisms of $��S�$ acting primitively on both points and lines of $��S�$, we show that if $��\alpha �\; �\le �\; �60�$ then $��G�$ must be almost simple.