Degree sequence

Degree sequence --- степенная последовательность.

For a graph [math]\displaystyle{ G }[/math], its degree sequence [math]\displaystyle{ d_{1} \geq d_{2} \geq \ldots \geq d_{n} }[/math] is the ordered sequence of the degrees of its vertices. A sequence [math]\displaystyle{ d_{1} \geq d_{2} \geq \ldots \geq d_{n} }[/math] with [math]\displaystyle{ n-1 \geq d_{1} }[/math] is a graphic sequence of numbers if there is a graph having [math]\displaystyle{ D_{1}, \ldots, d_{n} }[/math] as its degree sequence.

See also

• Havel -- Hakimi criterion, Erd\"{os -- Gallai criterion}.