Graph‐theoretic characterization of the matrix property of full irreducibility without using a transversal | Zendy

Kevorkian Aram K. | Zendy

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Graph‐theoretic characterization of the matrix property of full irreducibility without using a transversal

Author(s) -

Kevorkian Aram K.

Publication year - 1979

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190030207

Subject(s) - irreducibility , mathematics , transversal (combinatorics) , bipartite graph , combinatorics , line graph , discrete mathematics , matrix (chemical analysis) , graph , pure mathematics , mathematical analysis , materials science , composite material

In this paper we introduce the notion of strongly connected polygons in the line graph of a bipartite graph. We use this notion to give a necessary and sufficient condition for a matrix Y to be fully irreducible without the need to construct a transversal of Y. In addition, we show that the notion of strongly connected polygons forms the basis of a general theory that may be used for finding all the cycles in the directed graph of a fully irreducible matrix and for constructing all the nonzero transversals of a fully irreducible matrix.

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