Fully Indecomposable and Nearly Decomposable Graphs
Keywords:Permanent, Partly Decomposable, Fully Indecomposable, Factor.
LetA be an n-square non-negative matrix. If A contains no s\times t zero submatrix, where s + t = n, then it is called fully indecomposable. Also, a graph G is said to be fully indecomposable if its adjacency matrix is fully indecomposable. In this paper we provide some necessary and sucient conditions for a graph to be fully indecomposable. Among other results we prove that a regular connected graph is fully indecomposable if and only if it is not bipartite.
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