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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Varmazyar, Rezvan
Department of Mathematics‎, ‎Khoy Branch‎, ‎Azad University‎, ‎Khoy‎, ‎Iran
Electrical & Electronics Engineering

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Minimally 4-restricted edge connected graphs Kamyab, Khalid; Ghasemi, Mohsen; Varmazyar, Rezvan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.2.10

Abstract

Suppose that G is minimally 4-restricted edge connected graph without triangle, δ(G) ≥ 2 and α4(G) ≥ 6. Suppose that A is a λ4-atom of G such that for each path of length 3 in A, say P3 = xyz, we have dA(y) − 1 = dA−{x,y,z}(y), where x ∼ y ∼ z. In this paper, under these assumptions, we show that all atoms of G are trivial.
Co-Authors Ghasemi, Mohsen Kamyab, Khalid