Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that in a digraph without parallel edges, the number of pairs of vertices having a common in-neighbor or a common out-neighbor is at least the number of edges. We deduce that for any simple group-grading, the dimension of the trivial component is maximal.
|Number of pages||5|
|State||Published - 6 Jan 2015|
Bibliographical notePublisher Copyright:
© 2014 Elsevier B.V.
- Mutually neighbored vertices
- Simply-graded algebras
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics