3-Regular graphs

Asymptotic results for labelled regular graphs are more tractable. Wormald [WorN78] showed that the number of r-rcgular graphs on p labelled vertices is asymptotic to... 

B0IB8O Bollobas, B. A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Europ. J. Comb. 1 (1980) 311-316. 

Figure 4 A 3-regular graph of size 4 together with a possible edge-colouring the edge-colouring matrices correspond to entries having the same colour in the adjacency matrix A of the graph.

In brief, a discrete quantum random walk comprises of an in general d - regular graph G with n vertices (where lattices are favoured in the literature) and a spin degree of freedom, where the spin can take up d different states. A quantum state at a vertex v with spin i is then... 

If all vertices in a graph have the same degree, then the graph is called regular graph, otherwise irregular graph. 

Nikolic, S., Trinajstic, N. and Ivanis, S. (1999a) The connectivity indices of regular graphs. Croat. Chem. Acta, 72, 875-883. 

Yang, Y., Lin, J. and Wang, C. (2002) Small regular graphs having the same path layer matrix. J. Graph Theory, 39, 219-221. 

An important subgraph of fCy is the cycle Cm this being a regular graph of degree two. 

M. Meringer, J. Graph Theory, 30, 137 (1999). Fast Generation of Regular Graphs and... 

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