Graph magnitude homology via algebraic Morse theory

Abstract

We compute magnitude homology of various graphs using algebraic Morse theory. Specifically, we (1) give an alternative proof that trees are diagonal, (2) identify a new class of diagonal graphs, (3) prove that the icosahedral graph is diagonal, and (4) compute the magnitude homology of cycles. These results answer several questions of Hepworth and Willerton [HW17].

References in corpus (1)

• Magnitude homology of enriched categories and metric spaces

Cited by in corpus (6)

• Persistent Magnitude
• Magnitude homology of enriched categories and metric spaces
• Entropy and Diversity: The Axiomatic Approach
• Girth, magnitude homology, and phase transition of diagonality
• Geometric approach to graph magnitude homology
• Magnitude homology of graphs and discrete Morse theory on Asao-Izumihara complexes