#### Filter Results:

#### Publication Year

1975

2015

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

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)

A number of combinatorial problems are treated using properties of abelian nilpotent-and idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle is known to be NP-complete. By considering entries of Λ k , where Λ is an appropriate nilpotent adjacency matrix, the k-cycles… (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)

Questions about a graph's connected components are answered by studying appropriate powers of a special " adjacency matrix " constructed with entries in a commutative algebra whose generators are idempotent. The approach is then applied to the Erdös-Rényi model of sequences of random graphs. Developed herein is a method of encoding the relevant information… (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)

Classical approaches to multi-constrained routing problems generally require construction of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the notion of constrained path algebras and their application to multi-constrained path problems. The inherent combinatorial properties of these algebras make them useful for… (More)