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A zonotope associated with graphical degree sequences. (English) Zbl 0737.05057
Applied geometry and discrete mathematics, Festschr. 65th Birthday Victor Klee, DIMACS, Ser. Discret. Math. Theor. Comput. Sci. 4, 555-570 (1991).
[For the entire collection see Zbl 0726.00015.]
Author’s abstract: “Let \(D_ n\) denote the convex hull in \(\mathbb{R}^ n\) of all (ordered) degree sequences of simple \(n\)-vertex graphs. Using the fact that \(D_ n\) is a zonotope, an explicit generating functions is found for the number of these degree sequences. The \(f\)-vector of \(D_ n\) is found using Zaslavsky’s theory of signed graph colorings. Finally we give a generalization based on a result of Fulkerson, Hoffman, and MacAndrew.”.

MSC:
05C30 Enumeration in graph theory
52Bxx Polytopes and polyhedra