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While powers of the adjacency matrix of a finite graph reveal information about walks on the graph, they fail to distinguish closed walks from cycles. Using elements of an appropriate commutative, nilpotent-generated algebra, a " new " adjacency matrix can be associated with a random graph on n vertices and |E| edges of nonzero probability. Letting X k… (More)

Wireless sensor networks (WSN) are inherently multi - constrained. They need to preserve energy while offering reliable and timely data reporting for a non-negligible number of scenarios. This is particularly true when a node should decide which forwarder has to be chosen for routing a packet. Nevertheless, solving multi-constrained routing problems is… (More)

—An innovative minimal paths algorithm based on operator calculus in graded semigroup algebras is described. Classical approaches to routing problems invariably require construction of trees and the use of heuristics to prevent com-binatorial explosion. The operator calculus approach presented herein, however, allows such explicit tree constructions to be… (More)

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