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- Title
SOME RESULTS ON AN ALGEBRO-GEOMETRIC CONDITION ON GRAPHS.
- Authors
KULKARNI, AVI; MAXEDON, GREGORY; YEATS, KAREN
- Abstract
Paolo Aluffi, inspired by an algebro-geometric problem, asked when the Kirchhoff polynomial of a graph is in the Jacobian ideal of the Kirchhoff polynomial of the same graph with one edge deleted. We give some results on which graph–edge pairs have this property. In particular, we show that multiple edges can be reduced to double edges, we characterize which edges of wheel graphs satisfy the property, we consider a stronger condition which guarantees the property for any parallel join, and we find a class of series–parallel graphs with the property.
- Subjects
GRAPHIC methods; GRAPH theory; COMBINATORICS; JACOBIAN determinants; POLYNOMIALS; MATHEMATICAL models
- Publication
Journal of the Australian Mathematical Society, 2018, Vol 104, Issue 2, p218
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788717000106