Construction of constant resistance networks using the properties of two-dimensional regions with antisymmetry

A self-dual one-terminal-pair graph with respect to vertices (
i
and
j
) can be realized
4(p_{i} + p_{j})- 11
edges and
2(p_{i} + p_{j})-6
vertices for
p_{i} >3
and
p_{j} >3
, where
p_{i}
and
p_{j}
are the degrees of (
i
and
j
).