학술논문
Set-independence graphs of vector spaces and partial quasigroups.
Document Type
Journal
Author
Falcón, Raúl M. (E-SEVL-AM) AMS Author Profile; Gopinath, S. (6-SRSAIT-M) AMS Author Profile; Kalaimurugan, G. (6-TU-M) AMS Author Profile
Source
Subject
05 Combinatorics -- 05C Graph theory
05C75Structural characterization of families of graphs
20Group theory and generalizations -- 20N Other generalizations of groups
20N05Loops, quasigroups
05C75
20
20N05
Language
English
ISSN
2148838X
Abstract
Summary: ``As a generalization of independence graphs of vector spacesand groups, we introduce the notions of set-independence graphs ofvector spaces and partial quasigroups. The former are characterized forfinite-dimensional vector spaces over finite fields. Further, we provethat every finite simple graph is isomorphic to either the independencegraph of a partial quasigroup or an induced subgraph of the latter. Wealso prove that isomorphic partial quasigroups give rise to isomorphicset-independence graphs. As an illustrative example, all finite graphsof order $n\leq 5$ are identified with the independence graph of apartial quasigroup of the same order.''