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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.

Please help regarding this.

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.

Please help regarding this.

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.

Please help regarding this.