Graph of constant finite eccentricity

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This article defines a property that can be evaluated to true/false for any undirected graph, and is invariant under graph isomorphism. Note that the term "undirected graph" as used here does not allow for loops or parallel edges, so there can be at most one edge between two distinct vertices, the edge is completely described by the vertices it joins, and there can be no edge from a vertex to itself.
View other such properties

Definition

Suppose is a connected undirected graph. We say that is a graph of constant finite eccentricity if it satisfies the following equivalent conditions:

  1. is a graph of finite diameter and its radius equals its diameter.
  2. The eccentricity of every vertex of is equal to a fixed finite number.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
vertex-transitive finite connected graph
vertex-transitive graph of finite diameter

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
connected graph