Vol. 56, No. 1, 1975

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Simple separable graphs

R. H. Johnson

Vol. 56 (1975), No. 1, 143–158

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 degree sequence 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.

Mathematical Subject Classification 2000
Primary: 05C99
Received: 28 September 1973
Revised: 6 May 1974
Published: 1 January 1975
R. H. Johnson