# Tagged Questions

Studying graphs using algebra (for example, linear algebra and abstract algebra) as a tool.

2answers
991 views

### Automorphism group and congruences of the cube

I want to prove that the automorphism group of the cube is $\mathbb{Z}_2 \times S_4$, by using information about the congruences of a cube. By the cube, I mean the graph of the platonic solid, i.e. ...
1answer
252 views

### associativity in graph theory

Can anybody help me in clearing the facts how the associativity was proved in cartesian product of 3 graphs, and thus showing isomorphism. I can easily solve for the case when its two graphs. Taking ...
2answers
804 views

### Chromatic polynomial of a grid graph

I have the following graph with $nm$ vertices: ...
1answer
913 views

### The number of labelled graphs with all vertices of even degree

I have a graph exam tomorrow, and there is a problem that said number of graph with labeled vertices and all of them of even degree is $2^{n-1 \choose 2}$. According to that topic, it means the ...
3answers
2k views

### Why there are $11$ non-isomorphic graphs of order $4$?

I'm new to graph theory and I don't plan to become a serious student of graph theory either. My book suggests that there are $11$ non-isomorphic graphs of order $4$, but I can't see why. I know that ...
3answers
958 views

### Can I find the connected components of a graph using matrix operations on the graph's adjacency matrix?

If I have an adjacency matrix for a graph, can I do a series of matrix operations on the adjacency matrix to find the connected components of the graph?
2answers
178 views

### to clear doubt about basic definition in graph theory

Can anybody help me in clearing the doubt about hierarchical product of graphs. Its quite different from other graph products. Here is the screenshot and link how it is done. I know the rooted graph, ...
0answers
140 views

### Is there matrix representation of the line graph operator?

I had the need to calculate the adjacency matrix $L$ of the line graph of a certain planar $k$-regular graphs $G(n,e)$ ( $n$ vertices and $e=\frac k2 n$ edges) given its adjacency matrix $A_G$. Here I ...
2answers
83 views

### Example of non-commutative association scheme

I need an example of non-commutative association scheme of ordered 6. I tried to use the example in the book Handbook of Combinatorial Designs, Second Edition by Charles J. Colbourn‏،Jeffrey H. Dini ...
0answers
121 views

2answers
144 views

### Chromatic polynomial of a graph - might take a while

I'm currently struggling with graphs that require either adding edges, or removing them. Problem here being that the graphs I'm working on takes forever to complete and I don't really know if adding ...
0answers
58 views

2answers
219 views

### What is a cycle hypergraph?

What is a cycle hypergraph? Could someone give me good reference or illustrate with a few examples?