Some algebraic invariants of ideals associated with graph families

Hafsa Bibi (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)
Hanni Garminia (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)
. Irawati (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)
Asia Rauf (Department of Mathematics, Govt. College Women University Faisalabad, Pakistan)
Um- E- Aimen (Department of Mathematics, Govt. College Women University Faisalabad, Pakistan)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications

In this article, we study some algebraic invariants of monomial ideals associated with graphs. Specifically, we compute the depth and Stanley depth of edge ideals arising from sunlet graphs, cycle-related graphs, and wheel-related graphs. In addition, we show that the path ideal of length two in centipede-related graphs satisfies both the persistence and strong persistence properties.