ANALISIS PERAN PEREMPUAN DALAM MENANAMKAN NILAI-NILAI PENDIDIKAN ISLAM TERHADAP ANAK

All human beings are creatures of the one God. They are equal, regardless of cultural background. Therefore, they receive the same appreciation from God and that must be respected and glorified. Thus, discrimination based on gender, skin color, class, race, ethnicity, religion, and so on has no basis at all in the teachings of Tawhid. Only the level of taqwa to Allah is the measure of the difference. The concepts of biological and sociocultural differences between men and women view that biological differences between the two are considered natural, while social differences are considered cultural. Whatever the background of these differences, it is not a reason to justify each other because women have the same rights as men in all fields, including education, economy, social, culture, even law and defense and state security. Women deserve special rights. Women should have important roles as well as recognition in various aspects of life. Education for women is very important. Educating women is a fundamental and critical necessity, so they can play their role properly and correctly and give contribution as productive members of the society.

On non-adaptive majority problems of large query size

We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the problem has different variants, according to what the answers to the queries can be. These questions has attracted several researchers, but the focus of most research was the adaptive version, where queries are decided sequentially, after learning the answer to the previous query. Here we study the non-adaptive version, where all the queries have to be asked at the same time.

Transversals and Bipancyclicity in Bipartite Graph Families

A bipartite graph is called bipancyclic if it contains cycles of every even length from four up to the number of vertices in the graph. A theorem of Schmeichel and Mitchem states that for $n \geqslant 4$, every balanced bipartite graph on $2n$ vertices in which each vertex in one color class has degree greater than $\frac{n}{2}$ and each vertex in the other color class has degree at least $\frac{n}{2}$ is bipancyclic. We prove a generalization of this theorem in the setting of graph transversals. Namely, we show that given a family $\mathcal{G}$ of $2n$ bipartite graphs on a common set $X$ of $2n$ vertices with a common balanced bipartition, if each graph of $\mathcal G$ has minimum degree greater than $\frac{n}{2}$ in one color class and minimum degree at least $\frac{n}{2}$ in the other color class, then there exists a cycle on $X$ of each even length $4 \leqslant \ell \leqslant 2n$ that uses at most one edge from each graph of $\mathcal G$. We also show that given a family $\mathcal G$ of $n$ bipartite graphs on a common set $X$ of $2n$ vertices meeting the same degree conditions, there exists a perfect matching on $X$ that uses exactly one edge from each graph of $\mathcal G$.

2-Distance Strong b-coloring of Perfect 𝜟-ary Tree

A 2-distance 𝑏-coloring is a 2-distance coloring in which every color class contains a vertex which has a neighbor in every other color class. A 2-distance strong 𝑏-coloring (2𝑠𝑏- coloring) is a 2-distance coloring in which every color class contains a vertex 𝑢 such that there is a vertex 𝑣 in every other color class satisfying the condition that the distance between 𝑢 and 𝑣 is at most 2. The 2-distance 𝑏-chromatic number 𝜒2𝑏(𝐺) (2𝑏-number) is the largest integer 𝑘 such that 𝐺 admits a 2-distance 𝑏-coloring with 𝑘 colors and the 2-distance strong bchromatic number 𝜒2𝑠𝑏(𝐺) (2𝑠𝑏-number) is the maximum k such that 𝐺 admits a 2𝑠𝑏-coloring with 𝑘 colors. A tree with a special vertex called the root is called a rooted tree. A perfect 𝛥- ary tree, is a rooted tree in which all internal vertices are of degree 𝛥 and all pendant vertices are at the same level. In this paper, the exact bound of the 2𝑠𝑏-number of perfect 𝛥-ary tree are obtained.

Exact 2-Distance b-Coloring and Exact 2-Distance b-Continuity of Helm Graph 𝑯𝒏

An exact 2-distance coloring of a graph 𝐺 is a coloring of vertices of 𝐺 such that any two vertices which are at distance exactly 2 receive distinct colors. An exact 2-distance chromatic number𝑒2(𝐺) of 𝐺 is the minimum 𝑘 for which 𝐺 admits an exact 2-distance coloring with 𝑘 colors. A 𝑏-coloring of 𝐺 by 𝑘 colors is a proper 𝑘-vertex coloring such that in each color class, there exists a vertex called a color dominating vertex which has a neighbor in every other color class. A vertex that has a 2-neighbor in all other color classes is called an exact 2-distance color dominating vertex (or an 𝑒2-cdv). Exact 2-distance 𝑏-coloring (or an 𝑒2𝑏-coloring) of 𝐺 is an exact 2-distance coloring such that each color class contains an 𝑒2- cdv. An exact 2-distance 𝑏-chromatic number (or an 𝑒2𝑏-number) 𝑒2𝑏(𝐺) of 𝐺 is the largest integer 𝑘 such that 𝐺 has an 𝑒2𝑏-coloring with 𝑘colors. If for each integer𝑘, 𝑒2(𝐺) ≤ 𝑘 ≤ 𝑒2𝑏(𝐺), 𝐺 has an 𝑒2𝑏-coloring by 𝑘 colors, then 𝐺 is said to be an exact 2-distance 𝑏- continuous graph. In this paper, the 𝑒2𝑏-number𝑒2𝑏(𝐻𝑛)of the helm graph 𝐻𝑛is obtained and 𝑒2𝑏-continuity of 𝐻𝑛is discussed.

The Dominator Edge Coloring of Graphs

Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .

Analytical modeling on the coloring of certain graphs for applications of air traffic and air scheduling management

Purpose The purpose of this paper is to assess the application of graph coloring and domination to solve the airline-scheduling problem. Graph coloring and domination in graphs have plenty of applications in computer, communication, biological, social, air traffic flow network and airline scheduling. Design/methodology/approach The process of merging the concept of graph node coloring and domination is called the dominator coloring or the χ_d coloring of a graph, which is defined as a proper coloring of nodes in which each node of the graph dominates all nodes of at least one-color class. Findings The smallest number of colors used in dominator coloring of a graph is called the dominator coloring number of the graph. The dominator coloring of line graph, central graph, middle graph and total graph of some generalized Petersen graph P_(n ,1) is obtained and the relation between them is established. Originality/value The dominator coloring number of certain graph is obtained and the association between the dominator coloring number and domination number of it is established in this paper.

b-Chromatic Sum and b-Continuity Property of Some Graphs

A b-coloring of a graph [Formula: see text] is a proper coloring of the vertices of [Formula: see text] such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the largest integer [Formula: see text] such that [Formula: see text] has a b-coloring with [Formula: see text] colors. The b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text], is introduced and it is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for any [Formula: see text] in a b-coloring of [Formula: see text] using [Formula: see text] colors. A graph [Formula: see text] is b-continuous, if it admits a b-coloring with [Formula: see text] colors, for every [Formula: see text]. In this paper, the [Formula: see text]-continuity property of corona of two cycles, corona of two star graphs and corona of two wheel graphs with unequal number of vertices is discussed. The b-continuity property of corona of any two graphs with same number of vertices is also discussed. Also, the b-continuity property of Mycielskian of complete graph, complete bipartite graph and paths are discussed. The b-chromatic sum of power graph of a path is also obtained.

A note on global dominator coloring of graphs

Global dominator coloring of the graph [Formula: see text] is the proper coloring of [Formula: see text] such that every vertex of [Formula: see text] dominates atleast one color class as well as anti-dominates atleast one color class. The minimum number of colors required for global dominator coloring of [Formula: see text] is called global dominator chromatic number of [Formula: see text] denoted by [Formula: see text]. In this paper, we characterize trees [Formula: see text] of order [Formula: see text] [Formula: see text] such that [Formula: see text] and also establish a strict upper bound for [Formula: see text] for a tree of even order [Formula: see text] [Formula: see text]. We construct some family of graphs [Formula: see text] with [Formula: see text] and prove some results on [Formula: see text]-partitions of [Formula: see text] when [Formula: see text].