# Questions tagged [graph-isomorphism]

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• 369
1 vote
88 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 ...
• 253
512 views

### How similar is the Goldwasser-Sipser Set Lower Bound Protocol to the Hashcash/Bitcoin Proof-of-Work?

Given a hash function $H:\{0,1\}^*\rightarrow\{0,1\}^n$, a difficulty $d\in\mathbb{N}$, and data $D\in\{0,1\}^*$, the framework of the Hashcash/Bitcoin Proof-of-Work entails finding a nonce $c$ such ...
• 253
59 views

### Polynomial-time algorithm for Graph Isomorphism in case of Maximum Constrained Maximum Degree

From Wolfram: A polynomial time algorithm is however known for planar graphs (Hopcroft and Tarjan 1973, Hopcroft and Wong 1974) and when the maximum vertex degree is bounded by a constant (Luks ...
• 331
170 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 ...
• 176
67 views

### Algorithm for getting symetric vertex sets of undirected graph

For my application problem, I am searching for an algorithm that can find all symmetric vertex sets of an undirected labeled graph. My definition of symmetric vertex set is: Let $G$ be a graph with ...
• 325
138 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 ...
• 131
168 views

### Literature about a naive approach to graph isomorphism by inspecting polynomials of adjacency matrices

I describe an approach to graph isomorphism which probably has false positives, and I am curious whether there is literature indicating that it does not work. Given two adjacency matrices $G, H$, an ...
• 4,167
10k views

### Subgraph isomorphism reduction from the Clique problem

I was trying to understand the Wikipedia proof for NP-completeness of subgraph isomorphism by reduction from the clique problem. It's really just one sentence: Let $H$ be the complete graph $K_k$; ...
• 297
103 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 ...
• 225
1 vote
203 views

### Find Mapping Node in a Graph

Given two large directed graphs (may have loops and lonely nodes) A and B. They are structurally similar. If we give a node in Graph A, how to find the corresponding one in Graph B? Finally, we need ...
• 113
194 views

### Efficient algorithm for graph canonization for directed acyclic graphs?

I'm interesting in generating directed acyclic graphs (see here, for example). As part of this search, I'm curious if there are any efficient algorithms for determining a canonization of a directed ...
• 221
810 views

### Generating all directed acyclic graphs with constraints

I am interested in listing all the unlabeled1 acyclic digraphs with n vertices which satisfy some additional constraints, such as (a) the resulting graph is connected and (b) except for ...
• 221
243 views

### Automorphism of a Graph with a given Set of Permutations

Given a graph $H$. A set of permutations $\alpha$ which contains permutations of vertices of $H$. The permutation set $\alpha$ has automorphisms of subgraph $H_1, H_2,..... H_x$ where $x$ is the ...
• 281
131 views

### If graph isomorphism yields a polynomial time algorihtm

Greeting I'm studying computing theory and are trying to grasp the concept of complexity classes. If graph isomorphism (suspected NPI) turns out to have polynomial time solution. What possible ...
• 77
Given a $2n$ vertex undirected graph whose vertices are partitioned arbitrarily in pairs to say WLOG $(1,2)$, $(3,4)$, $\dots$, $(2n-1,2n)$. Call these vertices pairs as super vertices. Call two such ...