  A large amount of research activity in power systems areas has focused on
developing computational methods to solve load flow equations where a key
question is the maximum number of isolated solutions.Though several concrete
upper bounds exist, recent studies have hinted that much sharper upper bounds
that depend the topology of underlying power networks may exist. This paper
establishes such a topology dependent solution bound which is actually the best
possible bound in the sense that it is always attainable. We also develop a
geometric construction called adjacency polytope which accurately captures the
topology of the underlying power network and is immensely useful in the
computation of the solution bound. Finally we highlight the significant
implications of the development of such solution bound in solving load flow
equations.
