a class of kirchhoff type systems with nonlinear boundary conditions considered in this paper. by using the method of nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

This paper deals with the length of a Robertson–Seymour’s tree-decomposition. The tree-length of a graph is the largest distance between two vertices of a bag of a tree-decomposition, minimized over all tree-decompositions of the graph. The study of this invariant may be interesting in its own right because the class of bounded tree-length graphs includes (but is not reduced to) bounded chordal...

We prove the following bound for a k regular graph on n vertices with nontrivial eigenvalues from the interval r s n k rs k r k s Equality holds if and only if the graph is strongly regular with eigenvalues in fk s rg Nonbipartite distance regular graphs with diameter d and eigenvalues k d whose local graphs satisfy the above bound with equality for s b and r b d are called tight graphs and are...

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric...