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Foundations of electrical network theory
Directedgraph solutions of linear algebraic equations
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1-factor 1-factorial connections 2-trees associated directed graph bipartite graph branch Chen Coates graph columns completes the proof components compute connected graph consider cotrees cutset defined Definition degree pairs denoted determinant directed circuits directed graph obtained directed path directed trees directed-edge directed-tree edge train edge-disjoint edges of G electrical network elements equicofactor matrix Euler line example exists follows formulas function Gc(A graph G graph of fig graph theory graph transmission incidence matrix integers invariant Lemma Let G linear linearly independent major submatrices Mason graph n-node network theory node set nonnegative integers nonsingular null graph number of directed number of edges obtained from G parallel edges planar graph presented in fig realizable reference node respectively result s)-digraph second-order cofactors sectional subgraph self-loops semifactors shown in fig submatrix subset symbol system of equations Theorem topological transformation trees of G two-port network undirected vector voltage zero