On Algebraic Aspects of Spanning Complexes

Abstract

In this thesis the main motive is to characterize some of the algebraic and combinatorial properties of spanning forest complexes Δs(G) of some simple finite disconnected graphs G. Spanning forests complexes play a key role in algebraic, topological and geometric combinatorics but, as compared to simplicial complexes, little is known about their geometric and combinatorial structure. We characterize some algebraic properties of forests complexes related to different book graphs on fixed ground set. We provide the characterization of f-vector for the spanning forest complex of k disjoint copies of a book graph.