Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  introduce the notion of strongly connected polygons in the line graph of a bipartite graph.  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,  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.
['Aram K. Kevorkian']
I am writing a research paper on a idea Graph-theoretic characterization of the matrix property of full irreducibility without using a transversal
[{"from": "human", "value": "I am writing a research paper on a idea Graph-theoretic characterization of the matrix property of full irreducibility without using a transversal"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  introduce the notion of strongly connected polygons in the line graph of a bipartite graph.  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,  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."}]