Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

Dimension and Coloring alongside Domination in Neutrosophic Hypergraphs

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

PEMILIHAN KARIR PADA PEGAWAI GENERASI MILLENIAL (STUDI KASUS : PEGAWAI PT XYZ)

PT XYZ is a company engaged in the field of production and services that has Human Resources spread throughout Indonesia. In this study, the object of observation is the employee in the East Java Unit which has a total of 2,300 personnel with the composition of the Millennial Generation (born 1981-1994) of 51% as the dominating number of employees in PT XYZ. The results of an interest survey conducted on 698 structural employees at the Basic Supervisor level (managerial type career) at PT XYZ East Java Unit, showed that 25% or 171 employees of the millennial generation chose functional careers (type of expertise). This phenomenon is then explored further in the research objectives, namely what factors influence career selection in millennial generation employees. This research is a qualitative research that uses the interview method. The result is that there are two factors that influence career choice, namely responsibility and type of work. Keywords : Millenials, Careers, Qualitative

On Locating-Dominating Set of Regular Graphs

Let G be a simple, connected, and finite graph. For every vertex v ∈ V G , we denote by N G v the set of neighbours of v in G . The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ V G such that every two distinct vertices u , v ∈ V G \ W satisfies ∅ ≠ N G u ∩ W ≠ N G v ∩ W ≠ ∅ . A graph G is called k -regular graph if every vertex of G is adjacent to k other vertices of G . In this paper, we determine the locating-dominating number of k -regular graph of order n , where k = n − 2 or k = n − 3 .

Computing the split domination number of grid graphs

<p>A set <em>D</em> - <em>V</em> is a dominating set of <em>G</em> if every vertex in <em>V - D</em> is adjacent to some vertex in <em>D</em>. The dominating number γ(<em>G</em>) of <em>G</em> is the minimum cardinality of a dominating set <em>D</em>. A dominating set <em>D</em> of a graph <em>G</em> = (<em>V;E</em>) is a split dominating set if the induced graph (<em>V</em> - <em>D</em>) is disconnected. The split domination number γ<em>_s</em>(<em>G</em>) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we have<br />obtained the exact values of γ<em>s</em>(<em>G_m;n</em>); <em>m</em> ≤ <em>n</em>; <em>m,n</em> ≤ 24:</p>

Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs

Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set S of a graph G=(V,E) is the set of vertices that dominates G, and for any i,j∈ V(G) N(i)∩S≠N(j)∩S is satisfied. The set S is called the OLD-set of G. The cardinality of the set S is called open locating-dominating number and denoted by γold(G). In this paper, we computed exact values of the prism and prism-related graphs, and also the exact values of convex polytopes of Rn and Hn. The upper bound is determined for other classes of convex polytopes. The graphs considered here are well-known from the literature.

Dominating Number on Icosahedral-Hexagonal Network

In this paper, we deal with the dominating set and the domination number on an icosahedral-hexagonal network. We will consider all cases of successive halving of the edges of triangles that are the sides of icosahedrons and thus obtain icosahedral-hexagonal networks.

Automorphism Group and Other Properties of Zero Component Graph over a Vector Space

In this paper, we introduce an undirected simple graph, called the zero component graph on finite-dimensional vector spaces. It is shown that two finite-dimensional vector spaces are isomorphic if and only if their zero component graphs are isomorphic, and any automorphism of a zero component graph can be uniquely decomposed into the product of a permutation automorphism and a regular automorphism. Moreover, we find the dominating number, as well as the independent number, and characterize the minimum independent dominating sets, maximum independent sets, and planarity of the graph. In the case that base fields are finite, we calculate the fixing number and metric dimension of the zero component graphs and determine vector spaces whose zero component graphs are Hamiltonian.