@article{Haq2025, 
author = {Ahtsham Ul Haq and Muhammad Usman Rashid and Muhammad Ishaq},
title = {Algebraic invariants of edge ideals from strong products of paths and cycles},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29650-29663},
keywords = {edge ideal, depth, projective dimension, stanley depth, Castelnuovo-Mumford regularity, Krull dimension, Cohen–Macaulay rings},
url = {https://www.sciopen.com/article/10.3934/math.20251303},
doi = {10.3934/math.20251303},
abstract = {This paper investigates algebraic invariants of edge ideals associated with families of graphs constructed as the strong product of a path or cycle with the complete graph        K    m  , namely              P        γ    =      P    γ    ⊠      K    m   and              C        γ    =      C    γ    ⊠      K    m  . For an edge ideal    I  (      G    )  ⊂  ℜ in a polynomial ring over a field        K  , we derive explicit combinatorial formulas for key homological and ring-theoretic invariants of the quotient ring    ℜ      /    I  (      G    ). These include Castelnuovo-Mumford regularity, depth, Stanley depth, projective dimension, and Krull dimension. Furthermore, we characterize all Cohen–Macaulay graphs in defined families, providing a complete classification where    ℜ      /    I  (      G    ) is Cohen–Macaulay.}
}