How to draw a graph with 18 levels

Hello

I want to show the (valid) states of the river problem in the form of a graph in MATLAB and then apply search DFS on it, but the problem I have is how to draw a graph of this problem. First, I want to graph this problem using a cell, but The problem in the cell is that it is not possible to identify the child of a node. Do you have a special suggestion for this problem ??

https://en.wikipedia.org/wiki/River_crossing_puzzle

It is assumed that the initial state is that everyone is on the left (start) side of the figure

[1 1 1 1 1 11 11] and the right (destination) in the form of [0000000000]

For example, children will be the first case

[11000000] and [00000011] and .......

Please help