Abstract
The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Highlights
An operation or composition in a non-void set H is a function from HuH to H while a hyperoperation or hypercomposition is a function from HuH to the power set P (H) of H
A set H endowed with a hypercomposition “” is called hypergroupoid if xyz for all x, y in H, otherwise it is called partial hypergroupoid
A hypercomposition is called right closed if a ba for all a,b H and left closed if a ab for all a,b H
Summary
An operation or composition in a non-void set H is a function from HuH to H while a hyperoperation or hypercomposition is a function from HuH to the power set P (H) of H. The hypercomposition in a hypergroup H is right open if and only if a / a a for all a H , while it is left open if and only if a \ a a for all a H. If the hypercomposition in a hypergroup H is right or left open, all its elements are idempotent. In general graph is a set of points called vertices connected by lines called edges. A tree T is a simple, connected graph with no Massouros introduced in [9] another type of path hypercomposition in graphs and some relevant hypercompositions in automata
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
