PARTIALLY PRESCRIBED MATRICES ASSOCIATED TO DIRECTED GRAPHS
In this paper, we introduce the concept of partially prescribed matrix associated to a directed graph without multiple arcs and prove that two graphs are isomorphic if and only if the respective partially prescribed matrices are similar.
Conversely, given a partially prescribed square matrix we associate a directed graph to the given matrix. Moreover, we prove there exits an injective map between the set of all directed graphs without multiple arcs and the set of all partially prescribed square matrices.
Further, we introduce the concept of disjoint union of two square matrices and prove that for two directed graphs without multiple arcs the partially prescribed matrix associated to the disjoint union of coincides with the disjoint union of the partially prescribed matrices associated to respectively. Finally, for given two partially prescribed matrices we prove that the directed graph associated to the disjoint union of coincides with the disjoint union of the directed graphs associated to respectively.
directed graphs, partially prescribed matrix.