Pristine Transfinite Graphs and Permissive Electrical Networks

A transfinite graph or electrical network of the first rank is
obtained conceptually by connecting conventionally infinite graphs and
networks together at their infinite extremities. This process can be
repeated to obtain a hierarchy of transfiniteness whose ranks increase
through the countable ordinals. This idea, which is of recent origin,
has enriched the theories of graphs and networks with radically new
constructs and research problems.
The book provides a more accessible introduction to the subject that,
though sacrificing some generality, captures the essential ideas of
transfiniteness for graphs and networks. Thus, for example, some
results concerning discrete potentials and random walks on transfinite
networks can now be presented more concisely. Conversely, the
simplifications enable the development of many new results that were
previously unavailable.
Topics and features: *A simplified exposition provides an introduction
to transfiniteness for graphs and networks.*Various results for
conventional graphs are extended transfinitely. *Minty's powerful
analysis of monotone electrical networks is also extended
transfinitely.*Maximum principles for node voltages in linear
transfinite networks are established. *A concise treatment of random
walks on transfinite networks is developed. *Conventional theory is
expanded with radically new constructs.
Mathematicians, operations researchers and electrical engineers, in
particular, graph theorists, electrical circuit theorists, and
probabalists will find an accessible exposition of an advanced
subject.