scholarly journals A graph theoretic method for determining generating sets of prime ideals in quantum matrices

2011 ◽  
Vol 330 (1) ◽  
pp. 188-205 ◽  
Author(s):  
Karel Casteels
Keyword(s):  
Prime Ideals ◽  
Theoretic Method ◽  
Graph Theoretic ◽  
Quantum Matrices ◽  
Generating Sets

Some properties about the zero-divisor graphs of quasi-ordered sets

2019 ◽  
Vol 19 (04) ◽  
pp. 2050074
Author(s):  
Junye Ma ◽  
Qingguo Li ◽  
Hui Li
Keyword(s):  
Zero Divisor ◽  
Ordered Set ◽  
Line Graph ◽  
Prime Ideals ◽  
Complete Graphs ◽  
Ordered Sets ◽  
Graph Theoretic ◽  
Zero Divisor Graph ◽  
Complete Bipartite Graphs ◽  
Minimal Prime

In this paper, we study some graph-theoretic properties about the zero-divisor graph [Formula: see text] of a finite quasi-ordered set [Formula: see text] with a least element 0 and its line graph [Formula: see text]. First, we offer a method to find all the minimal prime ideals of a quasi-ordered set. Especially, this method is applicable for a partially ordered set. Then, we completely characterize the diameter and girth of [Formula: see text] by the minimal prime ideals of [Formula: see text]. Besides, we perfectly classify all finite quasi-ordered sets whose zero-divisor graphs are complete graphs, star graphs, complete bipartite graphs, complete [Formula: see text]-partite graphs. We also investigate the planarity of [Formula: see text]. Finally, we obtain the characterization for the line graph [Formula: see text] in terms of its diameter, girth and planarity.

scholarly journals A graph-theoretic method to find decentralized fixed modes of LTI systems

Automatica ◽  
2007 ◽  
Vol 43 (12) ◽  
pp. 2129-2133 ◽  
Author(s):  
Javad Lavaei ◽  
Amir G. Aghdam
Keyword(s):  
Theoretic Method ◽  
Graph Theoretic
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