# Questions tagged [automorphism]

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### Counterexample for Corneil's efficient algorithm for Graph Isomorphism

In the paper An Efficient Algorithm for Graph Isomorphism by Corneil and Gotlieb, 1970 a conjecture was stated upon which the stated algorithm relied for solving GI in polynomial time. Namely: that ...
863 views

### Relationship between symmetry and computational intractability?

The $k$-fixed point free automorphism problem asks for a graph automorphism which moves at least $k(n)$ nodes. The problem is $NP$-complete if $k(n)=n^c$ for any $c$>0. However, If $k(n)=O(\log n)$ ...
316 views

### Generating Graphs with Trivial Automorphisms

I'm revising some cryptographic model. To show its inadequacy, I've devised a contrived protocol based on graph isomorphism. It is "commonplace" (yet controversial!) to assume the existence of BPP ...
503 views

### Is “Is a permutation p an automorphism of a graph in my set?” NP-complete?

Suppose we have a set S of graphs (finite graphs, but an infinite number of them) and a group P of permutations that acts on S. Instance: A permutation p in P. Question: Does there exist a graph g in ...
566 views

### what are known bounds on complexity of nontrivial graph automorphism

Given any simple undirected graph G, it is nontrivial to determine if G has nontrivial (non-identity) automorphisms. But what are results on upper/lower bounds of this decision problem?
637 views

### Approximating non-trivial graph automorphism?

Graph automorphism is a permutation of graph nodes that induces a bijection on the edge set $E$. Formally, It is a permutation $f$ of nodes such $(u,v)\in E$ iff $(f(u),f(v))\in E$ Define an ...
303 views

### When polynomial GI implies polynomial (edge) colored GI?

Crossposted from MO. (edge) colored graph isomorphism is GI which preserves the colors (of edges if it is edge colored). There are several reductions using transformations/gadgets of (edge) colored ...
226 views

### Computing the edge orbits of a graph (and discussing definitions)

A (vertex) automorphism in a graph $G=(V,E)$ is a permutation $\sigma$ of the vertices that preserves adjacency, namely $\sigma(u) \sigma(v) \in E$ if and only if $uv \in E$. The automorphisms of a ...
280 views

### Complexity of counting poset automorphisms

A (finite) poset $P = (X, <)$, or partially ordered set, is a (finite) set $X$ equipped with a transitive antisymmetric relation $<$; it can be equivalently seen as a DAG $G = (X, E)$ that is ...
319 views

### Best lower bound for proof complexity of graph non-automorphism problem

Graph automorphism problem ( GA) of determining whether a graph has a nontrivial automorphism is a good candidate for a problem in NP-intermediate. I'm looking for references that study the ...
Consider an irreducible aperiodic Markov chain $M$, modeled as a connected directed graph with weighted edges. The existence of certain (graph) automorphisms on this Markov chain imply various ...