Counting edge numbers in bipartite graphs

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1. Oct 15, 2014

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,
...
Lk be the kth level of nk vertices.
Then a bipartite graph G12 is created by a combination of L1 and L2, G23 is of L2 and L3,...,Gij is of Li and Lj.

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

2. Oct 21, 2014