Edge-transitive graph: Difference between revisions
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An [[undirected graph]] is termed '''edge-transitive''' if it is either an [[empty graph]] or the induced action of its [[automorphism group of a graph|automorphism group]] on its edge set is [[groupprops:transitive group action|transitive]] on all edges. | An [[undirected graph]] is termed '''edge-transitive''' if it is either an [[empty graph]] or the induced action of its [[automorphism group of a graph|automorphism group]] on its edge set is [[groupprops:transitive group action|transitive]] on all edges. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions | |||
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| [[Weaker than::symmetric graph]] || || || || | |||
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Latest revision as of 03:22, 28 May 2012
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
An undirected graph is termed edge-transitive if it is either an empty graph or the induced action of its automorphism group on its edge set is transitive on all edges.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| symmetric graph |