Counting edge numbers in bipartite graphs

[Medicol]

Let L be the level number of a bipartite graph G, and so
L₁ be the first level of n₁ vertices,
L₂ be the second level of n₂ vertices,
...
L_k be the k^th level of n_k vertices.
Then a bipartite graph G₁₂ is created by a combination of L₁ and L₂, G₂₃ is of L₂ and L₃,...,G_ij is of L_i and L_j.

The number of edges in a bipartite graph is $m$x$n$. And the total number of the above network of bipartite graphs is $$\sum=n_1n_2+n_1n_3+...+n_1n_k+n_2n_3+...+n_2n_k+...+n_{k-1}n_k$$

• Is my sum above correct ?
• Are there any research publication concerning this bipartite graph node combination in networking optimization, genetic network, numerical research or graph theories that you know about ?

All the definitions are self-made, I have not been working with graphs for years, many basics are thus forgotten. Thank you. :D

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?