‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...

The characterization of distance-regular Cayley graphs originates from the problem identifying strongly regular graphs, or equivalently, partial difference sets. In this paper, a classification on dicyclic groups is obtained. More specifically, it shown that every graph group complete graph, multipartite non-antipodal bipartite with diameter 3 satisfying some additional conditions.

The regular number of a graph G denoted by reg(G) is the minimum number of subsets into which the edge set ofG can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an open problem in A. Ganesan et al. (2012) [3] about the complexity of determining the regular number of graphs. We show that computation of the regular number for...

It is well known that intra-regular semigroups (ordered semigroups) play an essential role in studying the structure of semigroups (ordered semigroups). In this paper we present a structure theorem referring to the decomposition of ordered semigroups into left strongly simple components, that is, into components, which are both simple and left quasi-regular. We prove, among others, that if an o...

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71 •) or with that of a regular octahedron (109 •). We study this model in the presence of a negative bending rigidity...

Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain variety itself permutohedral which is a toric variety. We give complete classification Fano weak regular in type A terms combinatorics functions. In particular, we show that if anticanonical bundle nef, then it fact nef big.

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

A graph G is k-ordered if for any sequence of k distinct vertices v1, v2, . . . , vk of G there exists a cycle in G containing these k vertices in the specified order. In 1997, Ng and Schultz posed the question of the existence of 4-ordered 3-regular graphs other than the complete graph K4 and the complete bipartite graph K3,3. In 2008, Meszaros solved the question by proving that the Petersen ...