Depth and Stanley depth of the edge ideals of the strong product of some graphs

Abstract

In this paper, we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated with classes of graphs obtained by the strong product of two graphs. We consider the cases when either both graphs are arbitrary paths or one is an arbitrary path and the other is an arbitrary cycle. We give exact formula for values of depth and Stanley depth for some subclasses. We also give some sharp upper bounds for depth and Stanley depth in the general cases.

Keywords

• Depth
• Stanley depth
• Stanley decomposition
• monomial ideal
• edge ideal
• strong product of graphs

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