scholarly journals The endomorphism semigroup of an endomapping of a finite set

2012 ◽  
Vol 31 ◽  
pp. 71-77
Author(s):  
Subrata Majumdar ◽  
Mohd Altab Hossain ◽  
Kalyan Kumar Dey
Keyword(s):  
Directed Graph ◽  
Endomorphism Semigroup ◽  
Finite Set

The structure of the semigroup of all endomorphisms of an endomapping of a finite set has been determined. This has been done by naturally representing the endomapping by a directed graph, and determining the structure of the endomorphism semigroup of this graph.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10310GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 71-77

scholarly journals Transversals in permutation groups and factorisations of complete graphs

2002 ◽  
Vol 65 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Gil Kaplan ◽  
Arieh Lev
Keyword(s):  
Permutation Group ◽  
Directed Graph ◽  
Sufficient Conditions ◽  
Combinatorial Problems ◽  
Permutation Groups ◽  
Transitive Permutation Group ◽  
Complete Graphs ◽  
Frobenius Theorem ◽  
Disjoint Cycles ◽  
Finite Set

Let G be a transitive permutation group acting on a finite set of order n. We discuss certain types of transversals for a point stabiliser A in G: free transversals and global transversals. We give sufficient conditions for the existence of such transversals, and show the connection between these transversals and combinatorial problems of decomposing the complete directed graph into edge disjoint cycles. In particular, we classify all the inner-transitive Oberwolfach factorisations of the complete directed graph. We mention also a connection to Frobenius theorem.

scholarly journals Sifat-Sifat Representasi Indekomposabel The Properties of Indecomposable Representations

2019 ◽  
Vol 8 (3) ◽  
Author(s):  
Vika Yugi Kurniawan
Keyword(s):  
Vector Space ◽  
Directed Graph ◽  
Linear Mapping ◽  
Sufficient Condition ◽  
Paper Study ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Indecomposable Representations ◽  
Finite Set ◽  
Necessary And Sufficient

A directed graph is also called as a quiver  where  is a finite set of vertices,  is a set of arrows, and  are two maps from  to . A representation  of a quiver  is an assignment of a vector space  to each vertex  of  and a linear mapping  to each arrow.  We denote by  the direct sum of representasions  and  of a quiver  . A representation  is called indecomposable if  is not ishomorphic to a direct sum of non-zero representations. This paper study about the properties of indecomposable representations. These properties will be used to investigate the necessary and sufficient condition of indecomposable representations.

scholarly journals Finite Homomorphism-Homogeneous Permutations via Edge Colourings of Chains

10.37236/2271 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Igor Dolinka ◽  
Éva Jungábel
Keyword(s):  
Directed Graph ◽  
Linear Order ◽  
Relational Structure ◽  
Traditional View ◽  
Linear Orders ◽  
Finite Set ◽  
Edge Colourings

A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation by a single linear order (considered as a directed graph with loops) whose non-loop edges are coloured in two colours, thereby `splitting' the linear order into two posets.

scholarly journals Finite Factors of Bernoulli Schemes and Distinguishing Labelings of Directed Graphs

10.37236/6 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Andrew Lazowski ◽  
Stephen M. Shea
Keyword(s):  
Automorphism Group ◽  
Lower Bound ◽  
Directed Graph ◽  
Directed Graphs ◽  
Bell Numbers ◽  
Undirected Graphs ◽  
Bernoulli Scheme ◽  
Finite Set ◽  
Finite Factor

A labeling of a graph is a function from the vertices of the graph to some finite set.  In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs.  Their definition easily extends to directed graphs.  Let $G$ be a directed graph associated to the $k$-block presentation of a Bernoulli scheme $X$.  We determine the automorphism group of $G$, and thus the distinguishing labelings of $G$.  A labeling of $G$ defines a finite factor of $X$.  We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of $X$.  We use the Bell numbers to find a lower bound for the number of finitarily Markovian finite factors of a Bernoulli scheme.  We show that demarcating labelings of $G$ are distinguishing.

On the Divisibility of Homogeneous Directed Graphs

1993 ◽  
Vol 45 (2) ◽  
pp. 284-294 ◽  
Author(s):  
M. El-Zahar ◽  
N. W. Sauer
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Isomorphic Copy ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Set ◽  
Necessary And Sufficient

AbstractLet be a finite set of finite tournaments. We will give a necessary and sufficient condition for the -free homogeneous directed graph to be divisible. That is, that there is a partition of into two classes such that neither of them contains an isomorphic copy of .

scholarly journals Convergence of Opinion Diffusion is PSPACE-Complete

2020 ◽  
Vol 34 (05) ◽  
pp. 7103-7110
Author(s):  
Dmitry Chistikov ◽  
Grzegorz Lisowski ◽  
Mike Paterson ◽  
Paolo Turrini
Keyword(s):  
Social Networks ◽  
Fixed Point ◽  
Directed Graph ◽  
Finite Set

We analyse opinion diffusion in social networks, where a finite set of individuals is connected in a directed graph and each simultaneously changes their opinion to that of the majority of their influencers. We study the algorithmic properties of the fixed-point behaviour of such networks, showing that the problem of establishing whether individuals converge to stable opinions is PSPACE-complete.

scholarly journals Structure of Endomorphism Semigroup of Endomappings of Some Particular Rooted Trees

2015 ◽  
Vol 39 (2) ◽  
pp. 169-175
Author(s):  
Mohd Altab Hossain
Keyword(s):  
Directed Graphs ◽  
Rooted Trees ◽  
Endomorphism Semigroup ◽  
Finite Set ◽  
Academy Of Sciences ◽  
Set Of Points

For an endomapping of a finite set of points lying on some rooted particular trees, endomorphism and endomorphism semigroup were studied. The main aim of this paper was to obtain the structure of the semigroup of all endomorphisms of the endomappings represented by directed graphs on particular types of rooted trees.Journal of Bangladesh Academy of Sciences, Vol. 39, No. 2, 169-175, 2015

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