New examples of W* and C* superrigid groups, strong rigidity for graph product groups, and cocycle superrigidity for joinings

2020 ◽  
Author(s):  
Alec Diaz-Arias
Keyword(s):  
Graph Product ◽  
Strong Rigidity

scholarly journals GRAPH PRODUCTS OF RIGHT CANCELLATIVE MONOIDS

2009 ◽  
Vol 87 (2) ◽  
pp. 227-252 ◽  
Author(s):  
JOHN FOUNTAIN ◽  
MARK KAMBITES
Keyword(s):  
Graph Products ◽  
Graph Product ◽  
General Characterization ◽  
Inverse Hull ◽  
Cancellative Monoids

AbstractOur first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialize to the case of the inverse hulls of graph monoids, obtaining what we call ‘polygraph monoids’. Among other properties, we observe that polygraph monoids are F*-inverse. This follows from a general characterization of those right cancellative monoids with inverse hulls that are F*-inverse.

Decompositions of graphs based on a new graph product

2019 ◽  
Vol 259 ◽  
pp. 31-40
Author(s):  
Antoon H. Boode ◽  
Hajo Broersma
Keyword(s):  
Graph Product

2-Distance chromatic number of some graph products

2020 ◽  
Vol 12 (02) ◽  
pp. 2050021
Author(s):  
Ghazale Ghazi ◽  
Freydoon Rahbarnia ◽  
Mostafa Tavakoli
Keyword(s):  
Chromatic Number ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Graph Products ◽  
Lexicographic Product ◽  
Graph Product ◽  
Minimum Number

This paper studies the 2-distance chromatic number of some graph product. A coloring of [Formula: see text] is 2-distance if any two vertices at distance at most two from each other get different colors. The minimum number of colors in the 2-distance coloring of [Formula: see text] is the 2-distance chromatic number and denoted by [Formula: see text]. In this paper, we obtain some upper and lower bounds for the 2-distance chromatic number of the rooted product, generalized rooted product, hierarchical product and we determine exact value for the 2-distance chromatic number of the lexicographic product.

The Growth Series of a Graph Product

1994 ◽  
Vol 26 (3) ◽  
pp. 268-272 ◽  
Author(s):  
I. M. Chiswell
Keyword(s):  
Graph Product ◽  
Growth Series

ORDERING GRAPH PRODUCTS OF GROUPS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250037 ◽  
Author(s):  
I. M. CHISWELL
Keyword(s):  
Graph Products ◽  
Graph Product ◽  
Free Products ◽  
Products Of Groups

It is shown that a graph product of right-orderable groups is right orderable, and that a graph product of (two-sided) orderable groups is orderable. The latter result makes use of a new way of ordering free products of groups.

Strong rigidity ofQ-rank 1 lattices

1973 ◽  
Vol 21 (4) ◽  
pp. 255-286 ◽  
Author(s):  
Gopal Prasad
Keyword(s):  
Strong Rigidity
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