Depth, Stanley Depth and Dimension of Edge Ideals Corresponding to Some Classes of Graphs

dc.contributor.author	Shahid, Malik Muhammad Suleman
dc.date.accessioned	2021-09-22T05:03:24Z
dc.date.available	2021-09-22T05:03:24Z
dc.date.issued	2020-09-08
dc.identifier.uri	http://10.250.8.41:8080/xmlui/handle/123456789/26210
dc.description	Supervised by Dr. Muhammad Ishaq	en_US
dc.description.abstract	This dissertation deals with the algebraic invariants such as depth and dimension as well as geometric invariant Stanley depth of some particular classes of graphs. Earlier, we have some general bounds for these invariants. The present thesis is primarily concerned with the value of depth and Stanley depth of edge ideals and their quotient rings (cyclic modules) related to some classes of graphs. In some cases we have an exact value, otherwise, we give very sharp bounds. In the end, we obtain a very strong lower bound for the dimension of the quotient rings of the edge ideals associated with these graphs. our results are general in nature, i.e., they hold for any non-negative integer. Also, we examine conjecture of Herzog and question of Rauf. 4	en_US
dc.language.iso	en_US	en_US
dc.publisher	School Of Natural Sciences National University of Sciences & Technology (NUST) Islamabad, Pakistan	en_US
dc.subject	Depth, Stanley Depth Dimension Edge Ideals Corresponding Some Classes Graphs	en_US
dc.title	Depth, Stanley Depth and Dimension of Edge Ideals Corresponding to Some Classes of Graphs	en_US
dc.type	Thesis	en_US