On the Graphs Related to Green Relations of Finite Semigroups

On Weierstrass semigroups arising from finite graphs

In 2007, Baker and Norine proved an analogue of the Riemann-Roch Theorem for finite graphs. Motivated by the Weierstrass semigroup of a point on a nonsingular projective curve X, it is natural to consider analogues for a vertex P on a finite, connected graph which has no loops. Let Hr(P ) be the set of nonnegative integers α such that r(αP ) = r((α − 1)P ) + 1, wherer(D) denotes the dimension o...

Semigroups related to subshifts of graphs

We characterise in terms of Zappa-Szép products a class of semigroups which arise from actions of groupoids on semigroups constructed from subshifts of graphs.

Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green’s relations when the semigroup is given by transformations on a finite set. Green’s relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of mag...

On the planarity of a graph related to the join of subgroups of a finite group

‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...

Decidability and Tameness in the Theory of Finite Semigroups