For a project about GPS systems, I'm trying to understand how can we see that there is a dead end thanks to an adjacency matrix.
I know that the adjacency matrix definition is
Assumed that $G=(V,E)$ is a simple graph, where $\left|V\right|=n$. Assumed also that the vertices number are arbitrarily numbered $v_1,\ldots,v_n$. The adjacency matrix $A$ of $G$ of this set of vertices is A with $$a_{ij}=\left\{\begin{array}{rl} 1 & \mbox{if } (v_i,v_j)\in E \\ 0 & \mbox{else.}\end{array}\right.$$
Here is the adjacency matrix I found corresponding on the top and on the side to the vertices $[1,2,9,10,11,12]$: \begin{pmatrix} 1 & 1 & 0 & 0 & 0 & 1 \\ 1& 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 & 1 \\ \end{pmatrix}
How can I know that some are dead end?
To my mind we can only know that thanks to the
The correct adjacency matrix is (observe that this is a directed graph) $$\begin{pmatrix}0&1&0&0&0&1\\ 0&0&0&0&0&0\\ 0&0&0&1&1&0\\ 0&0&0&0&1&0\\ 0&1&1&0&0&1\\ 0&0&0&0&0&0\end{pmatrix} $$ The rows corresponding to $2$ and $12$ are all zero, indicating that there is no way out.