PROBABILITY, GRAPHS AND ELECTRICAL NETWORKS

Explicit forms are presented for the probability that a random tree in a graph G contains any logically expressed set of edges, given that i t contains any other logically expressed set of edges. Edge sets may b e included or excluded, and may appear in a logical union or intersect ion. This probability is expressed in terms of various readily calcula ted or measured resistance values in a resistive electrical network ba sed on G. Explicit expressions are presented for the inspectional obta inment of resistance of the above type in a class of structures of con siderable application, including, for example, the n-cube used in larg e-scale computational assemblies.