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### How to construct a class of graphs satisfying a given matrix equation.

Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs satisfying the given matrix equation.

Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs satisfying the given matrix equation.
Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs matrices satisfying the given matrix equation.