The degree sequence of a graph is the sequence of the degrees of its vertices, arranged in non-decreasing order. If the degree sequence of a graph is unique, then the graph is reconstructible.

The degree sequence of a graph is the sequence of the degrees of its vertices, arranged in non-decreasing order. If the degree sequence of a graph is unique, then the graph is reconstructible.

A star graph is a tree with one central vertex and all other vertices connected to the central vertex. Star graphs are not reconstructible because their degree sequences are not unique.

The degree sequence of a graph is the sequence of the degrees of its vertices, arranged in non-decreasing order. If the degree sequence of a graph is unique, then the graph is uniquely reconstructible.

The degree sequence of a graph is the sequence of the degrees of its vertices, arranged in non-decreasing order. If the degree sequence of a graph is unique, then the graph is uniquely reconstructible.

A path graph is a tree with two end vertices and all other vertices having degree 2. Path graphs are uniquely reconstructible because their degree sequences are unique.

The edge degrees of a graph are the degrees of its edges, arranged in non-decreasing order. If the edge degrees of a graph are unique, then the graph is reconstructible from its edge degrees.

The edge degrees of a graph are the degrees of its edges, arranged in non-decreasing order. If the edge degrees of a graph are unique, then the graph is reconstructible from its edge degrees.

A star graph is a tree with one central vertex and all other vertices connected to the central vertex. Star graphs are not reconstructible from their edge degrees because their edge degree sequences are not unique.

The edge degrees of a graph are the degrees of its edges, arranged in non-decreasing order. If the edge degrees of a graph are unique, then the graph is uniquely reconstructible from its edge degrees.

The edge degrees of a graph are the degrees of its edges, arranged in non-decreasing order. If the edge degrees of a graph are unique, then the graph is uniquely reconstructible from its edge degrees.

A path graph is a tree with two end vertices and all other vertices having degree 2. Path graphs are uniquely reconstructible from their edge degrees because their edge degree sequences are unique.

The Laplacian spectrum of a graph is the spectrum of its Laplacian matrix. If the Laplacian spectrum of a graph is unique, then the graph is reconstructible from its Laplacian spectrum.

The Laplacian spectrum of a graph is the spectrum of its Laplacian matrix. If the Laplacian spectrum of a graph is unique, then the graph is reconstructible from its Laplacian spectrum.

A star graph is a tree with one central vertex and all other vertices connected to the central vertex. Star graphs are not reconstructible from their Laplacian spectra because their Laplacian spectra are not unique.