# What do we know about graph degree sequences?

The sequence of sizes of single vertex cuts of a graph is called its degree sequence. Is there an agreed-upon name for the sequence of sizes of k-vertex cuts? What can be said about two graphs which have the same sequences for all k

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This is the definition of degree sequence I have learned in my graph theory course: en.wikipedia.org/wiki/Degree_%28graph_theory%29#Degree_sequence Are we talking about the same thing? – Paul Jan 24 '12 at 10:15
@Paul: Yes. The point of the question is that the degree sequence records the number of edges connecting each vertex to the rest of the graph, which the OP generalizes to the sequence of numbers of edges connecting each set of $k$ vertices to the rest of the graph, and then asks what happens if $G$ and $H$ have the same generalized degree sequences for all $k$. – Louis Jan 24 '12 at 13:18
@Louis: Oh I see. Thank you for the explanation. – Paul Jan 24 '12 at 13:41