The paper includes the results of an extensive empirical study of broadcasting in small regular graphs using a stochastic search algorithm to approximate the broadcast time. Significant improvements on known results are obtained for cubic broadcast networks. We deduce that the Engel condition in an arbitrary associative ring is inherited by its group of units, and implies a semigroup identity. A minimal broadcast network is a communication network that can transmit a message originated at any node to all other nodes of the network in minimum time. The objective is to construct a network as sparse as possible satisfying the desired broadcasting time constraint.
Computational results illustrate the effectiveness of the proposed method.
This article shows that the two concepts are equivalent. We also provide new properties for center node sets, including bounds on the minimum size of a center node set, show how to reduce the number of center nodes of an mbn generated by a compound method, and propose an iterative compounding algorithm that generates the sparsest known mbns in many cases. Some open problems related to primeness of enveloping algebras are listed. The experiments lead to a rigorous proof, which we present. In 1990 Allen Bell presented a sufficient condition for the primeness of the universal enveloping algebra of a Lie superalgebra.