Depth and Stanley Depth of the Edge Ideals of <i>r</i>-Fold Bristled Graphs of Some Graphs

Abstract

In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king’s graphs, and circular king’s graphs.

Keywords

• depth
• Stanley depth
• projective dimension
• edge ideal
• r-fold bristled graph
• ladder graph