On Cayley Graphs of Inverse Semigroups

2006 ◽  
Vol 72 (3) ◽  
pp. 411-418 ◽  
Author(s):  
A.V. Kelarev
Keyword(s):  
Cayley Graphs ◽  
Inverse Semigroups

When is the cayley graph of a semigroup isomorphic to the cayley graph of a group

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Shoufeng Wang
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Inverse Semigroups ◽  
Graphs Of Groups ◽  
Cayley Graphs Of Semigroups ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

AbstractIt is well known that Cayley graphs of groups are automatically vertex-transitive. A pioneer result of Kelarev and Praeger implies that Cayley graphs of semigroups can be regarded as a source of possibly new vertex-transitive graphs. In this note, we consider the following problem: Is every vertex-transitive Cayley graph of a semigroup isomorphic to a Cayley graph of a group? With the help of the results of Kelarev and Praeger, we show that the vertex-transitive, connected and undirected finite Cayley graphs of semigroups are isomorphic to Cayley graphs of groups, and all finite vertex-transitive Cayley graphs of inverse semigroups are isomorphic to Cayley graphs of groups. Furthermore, some related problems are proposed.

A ROUTING ALGORITHM FOR THE CAYLEY GRAPHS GENERATED BY PERMUTATION GROUPS

2020 ◽  
Vol 21 (2) ◽  
pp. 187-194
Author(s):  
А. A. Kuznetsov ◽  
◽  
V. V. Kishkan ◽  
Keyword(s):  
Cayley Graphs ◽  
Routing Algorithm ◽  
Permutation Groups

scholarly journals A basis theorem for free inverse semigroups

1977 ◽  
Vol 49 (1) ◽  
pp. 172-190 ◽  
Author(s):  
P.R Jones
Keyword(s):  
Inverse Semigroups ◽  
Basis Theorem

Independent perfect dominating sets in semi-Cayley graphs

2021 ◽  
Author(s):  
Xiaomeng Wang ◽  
Shou-Jun Xu ◽  
Xianyue Li
Keyword(s):  
Cayley Graphs ◽  
Dominating Sets

scholarly journals Cayley Graphs Without a Bounded Eigenbasis

2020 ◽  
Author(s):  
Ashwin Sah ◽  
Mehtaab Sawhney ◽  
Yufei Zhao
Keyword(s):  
Cayley Graph ◽  
Orthonormal Basis ◽  
Cayley Graphs ◽  
The Other ◽  
Transitive Graph ◽  
Classic Result ◽  
Other Hand ◽  
Small Set ◽  
Vertex Transitive ◽  
Vertex Transitive Graph

Abstract Does every $n$-vertex Cayley graph have an orthonormal eigenbasis all of whose coordinates are $O(1/\sqrt{n})$? While the answer is yes for abelian groups, we show that it is no in general. On the other hand, we show that every $n$-vertex Cayley graph (and more generally, vertex-transitive graph) has an orthonormal basis whose coordinates are all $O(\sqrt{\log n / n})$, and that this bound is nearly best possible. Our investigation is motivated by a question of Assaf Naor, who proved that random abelian Cayley graphs are small-set expanders, extending a classic result of Alon–Roichman. His proof relies on the existence of a bounded eigenbasis for abelian Cayley graphs, which we now know cannot hold for general groups. On the other hand, we navigate around this obstruction and extend Naor’s result to nonabelian groups.

scholarly journals Tetravalent edge-transitive Cayley graphs of Frobenius groups

2021 ◽  
Vol 53 (2) ◽  
pp. 527-551
Author(s):  
Lei Wang ◽  
Yin Liu ◽  
Yanxiong Yan
Keyword(s):  
Cayley Graphs ◽  
Frobenius Groups ◽  
Edge Transitive

scholarly journals Inverse semigroups with idempotent-fixing automorphisms

2014 ◽  
Vol 89 (2) ◽  
pp. 469-474 ◽  
Author(s):  
João Araújo ◽  
Michael Kinyon
Keyword(s):  
Inverse Semigroups
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