Abstract
The purpose of this paper is to associate two-edge-connected graphs to a vector space of matrices. The fruitfulness of this association is shown by deriving various graph theoretic results via algebraic arguments on the associated vector space. The paper is divided into two sections. In the first section, an association between a vector space of matrices and two-edge-connected graphs is developed. The transfer of various properties of graphs to matrices and of matrices to graphs is then considered. In the second section the utility of the association developed in Section 1 is indicated by showing how the algebraic representation may be used, as a tool, to deduce rather interesting results concerning the structure of the associated graphs.
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