Details:
Title  Cayley digraphs of finite abelian groups and monomial ideals.  Author(s)  Ibeas Alvar, Gomez Domingo, Jaime Gutierrez  Type  Article in Journal  Abstract  In the study of doubleloop computer networks, the diagrams known as Lshapes arise as a graphical representation of an optimal routing for every graph's node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece of information, we can compute the graph's diameter and average minimum distance. That monomial ideal is the initial ideal of a certain lattice with respect to a graded monomial ordering. This result permits the use of Gröbner bases for computing the ideal and finding an optimal routing. Finally, we present a family of Cayley digraphs parametrized by their diameter d, all of them associated to irreducible monomial ideals.
 ISSN  08954801; 10957146/e 
URL 
http://epubs.siam.org/doi/abs/10.1137/050646056 
Language  English  Journal  SIAM J. Discrete Math.  Volume  21  Number  3  Pages  763784  Publisher  Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA  Year  2007  Edition  0  Translation 
No  Refereed 
No 
