NDLI: Spinorial Formulations of Graph Problems

Content Provider	Springer Nature Link
Author	Harris, Glenn M. Staples, G. Stacey
Copyright Year	2011
Abstract	Beginning with an arbitrary finite graph, various spinor spaces are constructed within Clifford algebras of appropriate dimension. Properties of spinors within these spaces then reveal information about the structure of the graph. Spinor polynomials are introduced and the notions of degrees of polynomials and Fock subspace dimensions are tied together with matchings, cliques, independent sets, and cycle covers of arbitrary finite graphs. In particular, matchings, independent sets, cliques, cycle covers, and cycles of arbitrary length are all enumerated by dimensions of spinor subspaces, while sizes of maximal cliques and independent sets are revealed by degrees of spinor polynomials. The spinor adjacency operator is introduced and used to enumerate cycles of arbitrary length and to compute graph circumference and girth.
Starting Page	59
Ending Page	77
Page Count	19
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	22
Issue Number	1
e-ISSN	16614909
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-04-27
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Spinors graphs cliques matchings cycles quantum probability Applications of Mathematics Mathematical Methods in Physics Physics Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Spinorial Formulations of Graph Problems