Moore graphs and beyond: A survey of the degree/diameter problem Page 1 Moore graphs
and beyond: A survey of the degree/diameter problem Mirka Miller School of Mathematical …

Given a simple connected graph G, let κ (n)[λ (n)] be the minimum cardinality of a set of
vertices [edges], if any, whose deletion disconnects G and every remaining component has …

Following Harary, the conditional connectivity (edge-connectivity) of a graph with respect to
a given graph-theoretic property is the minimum cardinality of a set of vertices (edges), if …

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 …

Abstract The super (resp., edge-) connectivity of a connected graph is the minimum
cardinality of a vertex-cut (resp., an edge-cut) whose removal does not isolate a vertex. In …

For a connected graph the restricted edge‐connectivity λ′(G) is defined as the minimum
cardinality of an edge‐cut over all edge‐cuts S such that there are no isolated vertices in G …

The matching preclusion number of a graph is the minimum number of edges whose
deletion results in a graph that has neither perfect matchings nor almost‐perfect matchings …

The star graph proposed by [1] has many advantages over the n-cube. However it suffers
from having large gaps in the number of possible vertices. The (n, k)-star graph was …

The super connectivity κ1 of a connected graph G is the minimum number of vertices whose
deletion results in a disconnected graph without isolated vertices; this is a more refined …

The super edge‐connectivity λ′ of a connected graph G is the minimum cardinality of an
edge‐cut F in G such that every component of G− F contains at least two vertices. Let Gi be a …