Nowadays, the problem of finding families graphs for which one may ensure existence a vertex-labeling and/or an edge-labeling based on certain class integers, constitutes challenge researchers in both number and graph theory. In this paper, we focus those vertex-labelings whose induced multiplicative assigns hyper totient numbers to edges graph. way, introduce characterize notions re...

Let S be a bipartite semigraph with |NXa(y)| ≥ 1 for every y ∈ Y . A vertex x ∈ X hyper dominates y ∈ Y if y ∈ Na(x) or y ∈ Na(NY a(x)). A subsetD ⊆ X is a hyper dominating set of S if every y ∈ Y is hyper dominated by a vertex ofD. A subsetD ⊆ X is called a minimal hyper dominating set of S if no proper subset of D is a hyper dominating set of S. The minimum cardinality of a minimal hyper domi...

This paper outlines the variational derivation of Lagrangian equilibrium equations for third-gradient materials, stemming from minimization total potential energy functional, and selection suitable dual variables to represent inner work in Eulerian configuration. Volume, face, edge wedge contributions were provided through integration by parts virtual repeated applications divergence theorem ex...

an improved mit bag model with hyper central interactions is used to calculate the staticproperties of hadrons containing u, d, s and c quarks. we present a theoretical approach to the internalstructure of three-body hyper central interacting quarks in a hadron, in which we take hadron as a bag.we discuss a few of the results obtained using a six-dimension harmonic oscilator (h.o) potential, ha...

One of the annual issues that has to be addressed in English football is producing a fixture schedule for the holiday periods that reduces the travel distance for the fans and players. This problem can be seen as a minimisation problem which must abide to the constraints set by the Football Association. In this study, the performance of selection hyper-heuristics is investigated as a solution m...

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzymultiply positive implicative hyper BCK-ideal. Moreov...

one of the most fundamental features of digital image and the basic steps in image processing, analysis, pattern recognition and computer vision is the edge of an image where the preciseness and reliability of its results will affect directly on the comprehension machine system made objective world. several edge detectors have been developed in the past decades, although no single edge detector...