The magnitude of a graph

Research output: Contribution to journalArticlepeer-review

Abstract

The magnitude of a graph is one of a family of cardinality-like invariants extending across mathematics; it is a cousin to Euler characteristic and geometric measure. Among its cardinality-like properties are multiplicativity with respect to cartesian product and an inclusion-exclusion formula for the magnitude of a union. Formally, the magnitude of a graph is both a rational function over Q and a power series over Z. It shares features with one of the most important of all graph invariants, the Tutte polynomial; for instance, magnitude is invariant under Whitney twists when the points of identification are adjacent. Nevertheless, the magnitude of a graph is not determined by its Tutte polynomial, nor even by its cycle matroid, and it therefore carries information that they do not.
Original languageEnglish
Pages (from-to)247-264
Number of pages19
JournalMathematical Proceedings of The Cambridge Philosophical Society
Volume166
Issue number2
Early online date27 Nov 2017
DOIs
Publication statusPublished - Mar 2019

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