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onsider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property

Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that A denotes the usual (0,1) adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues. Simply the question can be said as: Characterize all possible simple connected graphs on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues.

onsider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property

Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that A denotes the usual (0,1) adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues. Simply the question can be said as: Characterize all possible simple connected graphs on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues.

onsider Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property

Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that A denotes the usual (0,1) adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues. Simply the question can be said as: Characterize all possible simple connected graphs on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues.

please help regarding this problem.

Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property

Consider the class of all possible connected simple graphs on 6 vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that A denotes the usual (0,1) adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues. Simply the question can be said as: Characterize all possible simple connected graphs on 6 vertices such that if λ is an eigenvalue of A, then 1λ and 1λ both are eigenvalues.

please help regarding this problem.