No abstract

In this paper, we introduce a new class of diagram algebras which are subalgebras of cyclic G-Brauer algebras, called the Walled cyclic G-Brauer algebras denoted by W r,s (x), where r, s ∈ N and x is an indeterminate. The cellularity and the necessary and sufficient condition for W r,s (x) to be quasi-hereditary are established.

This paper introduces the concept of a bipolar fuzzy line graph of a bipolar fuzzy hypergraph and some of the properties of the bipolar fuzzy line graph of a bipolar fuzzy hypergraph are also examined.

In this paper, the concepts of regular bipolar fuzzy hypergraphs and totally regular bipolar fuzzy hypergraphs are introduced. We prove necessary and sufficient condition under which regular bipolar fuzzy hypergraphs and totally regular bipolar fuzzy hypergraphs are equivalent. Some properties of regular and totally regular bipolar fuzzy hypergraphs are examined. Regular bipolar fuzzy hypergraphs and totally regular bipolar fuzzy hypergraphs are compared through examples.

Here we focus on the construction of the planar automatons accepting two types of tableaux, namely, Le-diagrams and alternative tableaux. Then we associate a quadratic algebra Q with the constructed planar automaton and then by redefining the transition function by giving distinct labeling for distinct terms of the rewriting rule we get Q-tableaux. Finally, we give the proof of the equivalence between the tableaux accepting a planar automaton and Q-tableaux obtained, where the equivalence is given by Xavier Viennot in [8].