Graph theoretical properties of the node determinant of an LCR network

The node determinant
\Sigma A_{k} \Lambda^{k}
of an
LCR
network is given by the sum of the products of the element admittances of all the trees of the network. Some graph theoretical properties of the coefficients
\{A_{k}\}
are investigated where each
A_{k}
is represented as a function of the element values. The main results include the theorem that any three successive coefficients
A_{k}, A_{k+1}
, and
A_{k+2}
completely determine the network.