Abstract A $(k, g) $-cage is a $ k $-regular graph of girth $ g $ of minimum order. In this
survey, we present the results of over 50 years of searches for cages. We present the …

This is the only book on the topic of geometric configurations of points and lines. It presents
in detail the history of the topic, with its surges and declines since its beginning in 1876. It …

Let D be a graph or a digraph. If δ (D) is the minimum degree, λ (D) the edge-connectivity
and κ (D) the vertex-connectivity, then κ (D)⩽ λ (D)⩽ δ (D) is a well-known basic relationship …

We describe an implicit technique for enumerating structural choices in circuit optimization.
The restructuring technique relies on the symbolic statements of functional decomposition …

The degree/diameter problem for mixed graphs asks for the largest possible order of a
mixed graph with given diameter and degree parameters. Similarly the degree/geodecity …

Despite its popularity and widespread use, timeline visualisation suffers from shortcomings
which limit its use for displaying multiple data streams when the number of streams …

In this paper we give an upper bound for the order of ()-cages when 1 is not a prime power
and ¾ 6812. As an application we obtain new upper bounds for the order of cages when …

A (k, g)-cage is a graph that has the least number of vertices among all k-regular graphs with
girth g. It has been conjectured that the connectivity of each (k, g-cage is k, and a proof exists …

Abstract A (k; g)‐cage is a graph of minimum order among k‐regular graphs with girth g. We
show that for every cutset S of a (k; g)‐cage G, the induced subgraph G [S] has diameter at …

A note on the edge-connectivity of cages Page 1 A note on the edge-connectivity of cages
Ping Wang1∗ Baoguang Xu2 Jianfang Wang2 1 Department of Mathematics, Statistics and …