On the impossibility to construct diametrically critical graphs by extensions
Maximal Graphs with Given Connectivity and Edge-Connectivity
On Certain Edge-Critical Graphs of a Given Diameter
On the existence of critically n-connected graphs
Two classes of graphs related to extremal eccentricities
A graph is called an -graph if its periphery is equal to its center eccentric vertices . Further, a graph is called a -graph if . We describe -graphs and -graphs for small radius. Then, for a given graph and natural numbers , , we construct an -graph of radius having central vertices and containing as an induced subgraph. We prove an analogous existence theorem for -graphs, too. At the end, we give some properties of -graphs and -graphs.
On radially extremal graphs and digraphs, a survey
The paper gives an overview of results for radially minimal, critical, maximal and stable graphs and digraphs.
On the Existence of Certain Graphs with Diameter Two
On radially extremal digraphs
We define digraphs minimal, critical, and maximal by three types of radii. Some of these classes are completely characterized, while for the others it is shown that they are large in terms of induced subgraphs.
Note on the relation between radius and diameter of a graph
The known relation between the standard radius and diameter holds for graphs, but not for digraphs. We show that no upper estimation is possible for digraphs. We also give some remarks on distances, which are either metric or non-metric.
On Irreducible Graphs of Diameter Two without Triangles
On the Extension of Graphs with a Given Diameter without Superfluous Edges
Two-radially maximal graphs with special centers
Graphs related to diameter and center.
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