The relation between the
structure of a graph and the degrees of its vertices is a problem that has long
occupied graph theorists in one form or another. If the degrees of the vertices of a
graph are arranged in nonincreasing order the sequence obtained is the degreesequence of the graph. Thus the above problem is often formulated as “how does the
degree sequence affect the structure of the graph?” One approach is to discover which
graphs are determined up to isomorphism by their degree sequence. Following
Harary, these latter graphs and their degree sequences are called simple. In
simple graphs the effect of the degree sequence on structure is, in a good
sense, isolated. In this paper all simple graphs which are not blocks are
determined.
