SIGNED A-POLYNOMIALS OF GRAPHS AND POINCARÉ POLYNOMIALS OF REAL TORIC MANIFOLDS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 2, 2015, pp.467-481
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.2.467

Title & Authors

SIGNED A-POLYNOMIALS OF GRAPHS AND POINCARÉ POLYNOMIALS OF REAL TORIC MANIFOLDS

Seo, Seunghyun; Shin, Heesung;

Seo, Seunghyun; Shin, Heesung;

Abstract

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the polynomial , which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

Keywords

graph invariant;toric topology;Poincar polynomial;

Language

English

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