| dc.description.abstract |
In this thesis, we discuss the algebraic properties of path ideal It() associated to
a directed graph . As It() is a square free monomial ideal, it can be treated
as the facet ideal of one simplicial complex t() and non-face ideal of the other
simplicial complex N(It()). We give a systematic procedure to find the f-vector
F(It()). Afterwards, we introduce a special class of directed graphs called parallelseries
circuit graphs C
n(t, ). For C
n(t, ), we give the characterization of associated
primes of path ideal It+1(C
n(t, )) and for the Stanley-Reisner simplicial complex
associated to It(C
n(t, )), we show that
dim N(It+1(C
n(t, ))) = n − 2
where n is the number of vertices in C
n(t, ). |
en_US |