Questions tagged [graph-isomorphism]

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What is the current fastest algorithm for finding the maximum common subgraph?

First of all, it's my first time in #ComputerScience at StackExchange so, my apologies if I'm making some newbie mistake when asking this question. So, I'm currently researching algorithms for ...
4
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0answers
138 views

Generating all directed multigraphs

I am trying to find an algorithm that generates all directed multigraphs with a given number of vertices and arcs up to isomorphism (no two generated graphs should be isomorphic). I also want to allow ...
4
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96 views

Shortest paths in isomorphic graphs with different edge weights

I'm looking for a way to find the shortest paths from a source to all destinations in isomorphic undirected graphs with different edge weights. The only thing I can think of is using Dijkstra on each ...
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0answers
26 views

Complementary of graph invariant

Graph invariant is a property that holds for two isomorphic graphs. For example, degree sequence is graph invariant. We can write $d(G) \ne d(G') \Rightarrow G \ncong G'$, although $d(G) = d(G')$ ...
3
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51 views

Efficient approximation for find all the nodes and edges which match with some sub-tree in a graph

Let's suppose that I have a big digraph D and a small tree T (small w.r.t D), both directed, D can be connected or not, but T is connected. Here an example: Let's say that D is as follow: And T is ...
3
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270 views

Enumerate all non-isomorphic graphs of size n

I am trying to enumerate all non-isomorphic graphs of size n and found this question: Enumerate all non-isomorphic graphs of a certain size The accepted answer ...
2
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0answers
22 views

Subgraph isomorphism index/precomputation

I'm currently working on problem in which a set of graphs $T=\{t_1,\dots,t_n\}$ is given and fixed. Given a graph $m$ I want to check which of the $t_i$ are subgraphs of it, as quick as possible. Is ...
2
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50 views

Bipartite Planar Graph Isomorphism

I want a hueristic algorithm for the following problem. Here, $V(G)$, $E(G)$ respectively refer to the vertex set and edge set of a graph $G$. Input: two planar bipartite graphs, $G,H$ and a map $\...
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15 views

Why the soundness error in the $\mathrm{IP}$ of GNI can implicate $\mathrm{\Sigma_2} \subseteq \mathrm{\Pi_2}$ if GNI is co-NP-Complete?

PDF here shows a way to proof GI is NP-Complete $\implies \Sigma_2 = \Pi_2$. In the last step, it writes following: In other words, (1) is false in this case as required. Book Computational ...
2
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0answers
38 views

Are isomorphic (untyped) lambda expressions semantically equivalent?

"Isomorphic" is defined as having the same shape of syntax trees and the same bindings of variables. However, the variable names might be completely different. In other words, it is to say that we ...
2
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0answers
119 views

Generate all non-isomorphic bounded-degree rooted graphs of bounded radius

I need to generate/enumerate isomorphism classes of vertex-rooted graphs with the following properties. Let $\Delta$ be the maximal degree (say 3 for subcubic graphs) and $r$ the maximal distance of a ...
2
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68 views

Complexity of computing the first bits of a minimal permuted adjacency matrix

Given any graph $G$ on $V(G)=\{1,\dots,n\}$ and its adjacency matrix $$A(G)=\left(\matrix{ A_{1,1} & A_{1,2} & \dots & A_{1,n}\\ A_{2,1} & A_{2,2} & \dots & A_{2,n}\\ &&...
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30 views

Directed weighted multigraph isomorphism algorithms

Are there known algorithms for the isomorphism problem for directed weighted multigraphs? If not, could one be created simply by adapting existing algorithms for graphs or digraphs, or is it entirely ...
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104 views

Implementation of Babai's GI algorithm

Babai proved that there is a quasi-polynomial-time algorithm for graph isomorphism. Has anyone implemented this algorithm? I think the code will be easier to understand than his paper, because of the ...
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0answers
80 views

Interactive protocols for showing knots are “hard” to untie

Given two graphs $G_1$ and $G_2$, a zero-knowledge interactive protocol for a prover to convince a verifier that $G_1\not\cong G_2$ entails: The verifier choosing a random $i\in\{1,2\}$ The verifier ...
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94 views

Complexity lower bounds via Cook reductions

Karp reduction (polynomial-time many one) is used in complexity theory to define NP-completeness. However, Cook reductions (polynomial-time Turing) is more powerful and intuitive from information ...
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21 views

Name and complexity of a problem concerning metrics

Do you know the name of the following problem and can you give a reference for its complexity (especially the relation to $\mathsf{GraphIsomorphism}$ and/or other isomorphism/homomorphism problems)? ...
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36 views

Repeated subgraph isomorphism query for single-edge addition for bounded degree graphs

I have a source undirected colored graph $G$ and a base query graph $g$. I know $g$ is subisomorphic to $G$ and now I want to identify which edges I can add to $g$ to preserve subisomorphism. That is, ...
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161 views

brute-force canonical labelling of a simple graph

I am looking for an example that shows how to canonically label a graph using brute-force approach. An example with a 3 vertex or 4 vertex simple graph is preferred.
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106 views

Isomorphic induced subgraph problem using Courcelle's theorem

The isomorphic induced subgraph problem, is the problem of deciding whether, given two graphs $G$ and $H$, $G$ contains an induced subgraph isomorphic to $H$. Is there a proof using ...