In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

Consider a simple graph   on vertices and edges together with a total  labeling . Then ρ is called total edge irregular labeling if there exists a one-to-one correspondence, say  defined by  for all  where  Also, the value  is said to be the edge weight of . The total edge irregularity strength of the graph G is indicated by  and is the least  for which G admits   edge irregular h-labeling.  In this article,   for some common graph families are examined. In addition, an open problem is solved affirmatively.

 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin

in this paper we adopted ways for detecting edges locally classical prewitt operators and modification it are adopted to perform the edge detection and comparing then with sobel opreators the study shows that using a prewitt opreators