# Tag Info

### Combinatorica Functionality in Vers. 11.1.1

The problem is that you defined the Graph using M syntax and not Combinatorica syntax. For your example you should do: ...
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### How many graphs are there on 4 nodes with degrees 1, 1, 2, 2?

I had an old program lying around that will generate all realizations of a degree sequence. The first vertex will have degree equal to the first element in the input list, the 2nd degree equal to the ...
• 234k
Accepted

### Is there a Mathematica function that generates all ordered partitions?

You can use the resource function KSetPartitions as follows: ...
• 392k
Accepted

### Testing for Symmetry and Regularity in (Graph-Theoretic) Graphs

In general, if we first use GraphAutomorphismGroup to find the automorphism group of a graph, it is not hard to figure out if it acts transitively on vertices, ...
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### Replacement for GraphJoin

GraphComputationGraphJoin ...
• 392k

### How can I compute the chromatic number of a graph?

The IGraph/M package has an implementation of this. Example: << IGraphM g = RandomGraph[{10, 20}] Compute the chromatic number: ...
• 234k
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### FindShortestPathTree superseded by FindSpanningTree?

My IGraph/M package provides replacements for most of the graph theory functions of Combinatorica. It includes IGShortestPathTree: Example use on a weighted graph, ...
• 234k

### Testing for Symmetry and Regularity in (Graph-Theoretic) Graphs

IGraph/M 0.3.111 now has fast functions to test for all of these. Please look under Isomorphism -> Properties related to the automorphism group in the documentation. Regular: ...
• 234k
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### Counting k-colorings of a graph

The function FindProperColorings is now in the Wolfram Function Repository, and it lists all the proper k-colorings of a graph. https://resources.wolframcloud.com/FunctionRepository/resources/...

### Combinatorica Functionality in Vers. 11.1.1

Apparently, they killed it off without making an equivalent, so you'd have to re-implement an algorithm. documentation link is here: Upgrading from: Combinatorica In some cases, parameterized ...
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### Replacement for GraphJoin

The function you reference still works fine, but it is part of the Combinatorica package. You need to load the package first, and work with Combinatorica's own graph datatype. Combinatorica precedes ...
• 234k
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### Find independent tensor products using Young Tableaux

For those who are facing a similar problem, there is a beautiful package xTras which gives all possible contractions taking into account the symmetries of the ...
• 1,648
Accepted

### How many graphs are there on 4 nodes with degrees 1, 1, 2, 2?

4X4 adjacency matrices: am = Tuples[{0, 1}, {4, 4}]; 4X4 adjacency matrices with no self-loops: ...
• 392k

### FindShortestPathTree superseded by FindSpanningTree?

Thanks for that. Impressive. An alternative that might be better reflected in the documentation is to use FindShortestPath. ...
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### Counting k-colorings of a graph

Counting k-colorings of a graph Are you looking for https://en.wikipedia.org/wiki/Chromatic_polynomial of a graph? It can be computed with ChromaticPolynomial. <...
• 234k

### Find independent tensor products using Young Tableaux

Although xTras package is everything you need, I made a function (just for fun) that finds all the contraction of the product of 2-ranked tensors. It uses sort of ...
• 990
Accepted

### How can one calculate the co-normal (disjunctive/or) product of two graphs in Wolfram Language?

As noted in this Community post, the conormal/disjunctive product can be implemented like so for unweighted graphs: ...
Accepted

### Cycle index of a graph automorphism group

You can use CycleIndexPolynomial like so: ...
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### Orbits of a set $X$ under the action of cyclic permutation $T$

GroupOrbits[CyclicGroup[5], {{1, 1, 2, 3, 3}}, Permute] ...
• 392k
Accepted

### Up-to-date way to access Derangements (and other Combinatorica)

Please see Computational Discrete Mathematics by Pemmaraju and Skiena, pages 106 and 107. ...
• 15.2k
Accepted

The function FindProperColorings in the Wolfram Function Repository generates all proper k-colorings of a graph. https://resources.wolframcloud.com/FunctionRepository/resources/FindProperColorings

### How can I compute the chromatic number of a graph?

Very simple: ChromaticPolynomial[g]
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### Combinatorica Functionality in Vers. 11.1.1

IGraph/M already has replacements for most graph-related Combinatorica functions that are not yet covered by built-in functionality. Since IGraph/M 0.3.98, you can use ...
• 234k
Accepted

### Change VertexSize in ShowGraph from Combinatorica

The same way as in, e.g., ListPlot: ...
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### Multiple colors on a single graph edge?

trg = TransitiveReductionGraph[RelationGraph[UnsameQ@## && SubsetQ@##&, Subsets[Range@3]], VertexLabels -> "Name", EdgeShapeFunction->"Line"] <...
• 392k
Accepted

### How do I visualize the result of EdgeColoring[g]?

With IGraph/M, you can do the following: ...
• 234k