# D. DafikUniversitas Jember · Department of Mathematics Education

D. Dafik

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304

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Introduction

## Publications

Publications (304)

This study aims to identify students’ creative thinking skills in solving the problem of using chitosan as a natural preservative in processed meat. This research uses mixed methods, namely a combination of quantitative and qualitative research methods. We used quantitative research methods to analyze the results of student’s creative thinking skil...

Combinatorials require critical thinking procedures and convincing reasoning in the problem-solving process. Indicators of the combinatorial skills include identifying some cases, recognizing patterns from all cases, generalizing all cases, proving mathematically, and considering with other combinatorial problems. To apply higher-order thinking ski...

Resolving set has several applications in the fields of science, engineering, and computer science. One application of the resolving set problem includes navigation robots, chemical structures, and supply chain management. Suppose the set $ W = \left\{{s}_{1}, {s}_{2}, \dots , {s}_{k}\right\}\subset V\left(G\right) $, the vertex representations of...

Given that a graph G = (V, E). By an edge-antimagic vertex labeling of graph, we mean assigning labels on each vertex under the label function f : V → {1, 2, . . . , |V (G)|} such that the associated weight of an edge uv ∈ E(G), namely w(xy) = f(x) + f(y), has distinct weight. A path P in the vertex-labeled graph G is said to be a rainbow path if f...

\textbf{Background}: One of the topics of distance in graphs is the resolving set problem. Suppose the set $W=\{s_1,s_2,…,s_k\}\subset V(G)$, the vertex representations of $\in V(G)$ is $r_m(x|W)=\{d(x,s_1),d(x,s_2),…,d(x,s_k)\}$, where $d(x,s_i)$ is the length of the shortest path of the vertex $x$ and the vertex in $W$ together with their multipl...

The goal of this research is to produce RBL and STEM-based mathematics learning aids on the topic of Rainbow Vertex Antimagic Coloring. This type of research is referred to as R&D. (Research and Development). The goal of this research is to produce learning tools based on the Thiagarajan model, usually known as the 4-D model (four D model). This st...

For $k \geq 1$, in a graph $G=(V,E)$, a set of vertices $D$ is a distance $k$-dominating set of $G$, if any vertex in $V\setminus D$ is at distance at most $k$ from some vertex in $D$. The minimum cardinality of a distance $k$-dominating set of $G$ is the distance $k$-domination number, denoted by $\gamma_k(G)$. An ordered set of vertices $W=\{w_1,...

Creative thinking skills are very important in the 2lst era. The 2lst-century skills require a person to have 4C skills (Critical Thinking, Communication, Creative Thinking, and Collaboration) where creative thinking skills are in the 4C. We can integrate creative thinking skills into the teaching and learning process by implementing a specific mod...

Empowerment of STEM- research based learning is essential to developing student skills in the face of the industrial revolution by integrating science, technology, engineering and mathematic. The aim of the study was to design research-based learning activities with STEM cascara education on analyzing caffeine, trigonelline substance of cascara fer...

Let \(G=(V,E)\) be a graph with a vertex set \(V\) and an edge set \(E\). The graph \(G\) is said to be with a local irregular vertex coloring if there is a function \(f\) called a local irregularity vertex coloring with the properties: (i) \(l:(V(G)) \to \{ 1,2,...,k \} \) as a vertex irregular \(k\)-labeling and \(w:V(G)\to N,\) for every \(uv \i...

Given a graph G with vertex set V(G) and edge set E(G), for the bijective function f(V(G))→{1,2,⋯,|V(G)|}, the associated weight of an edge xy∈E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, the function f is called an edge-antimagic vertex labeling. A path P in the vertex-labeled graph G is said to be a rainbow x−y pa...

Mathematical literacy ability is a very important ability in learning mathematics. Through mathematical literacy, students are expected to be able to formulate, define, and interpret mathematics in various problem-solving contexts of everyday life. Mathematical literacy is also related to the international assessment standard, namely PISA, where PI...

After the Covid-19 pandemic, students are used to online learning, namely learning using gadgets. It is a fact that more students use their gadgets to play online games than educational sites. In playing online games students feel they are in a game that seems real. It's not uncommon for gamers to buy a VR box to play 3D games more realistically. V...

STEM approach in a research-based learning method that combines innovative research and learning. This research develop a research-based learning method based on STEM approach to improve students' metacognition skills in utilizing cascara fermentation with a magnetic field to produce health herbal teas. This research and development was employed th...

All graph in this paper are connected graph and simple graph. Let G = (V,E)be a connected graph. Rainbow vertex connection is the assignment of G that has interior vertices with different colors. The minimum number of colors from the rainbow vertex coloring in graph G is called rainbow vertex connection number. If wf(u) ̸= wf(v) for two different v...

All graph in this paper is simple and connected graph where $V(G)$ is vertex set and $E(G)$ is edge set. Let function $f : V(G)\longrightarrow \{0, 2,..., 2k_v\}$ as vertex labeling and a function $f: E(G)\longrightarrow \{1, 2,..., k_e\}$ as edge labeling where $k=max\{2k_v,k_e\}$ for $k_v,k_e$ are natural number. The weight of edge $ u,v\in E(G)...

Let [Formula: see text] be a simple graph and connected. A function [Formula: see text] is called vertex irregular [Formula: see text]-labeling and [Formula: see text] where [Formula: see text] The function of [Formula: see text] is called local irregular vertex coloring if every [Formula: see text] and [Formula: see text] vertex irregular labeling...

Combinatorial thinking is the process of obtaining multiple solutions for discrete problem-solving. Combinatorial thinking skills have several indicators: identifying several cases, recognizing patterns from all cases, generalizing all cases, proving mathematically, and considering other combinatorial problems. The learning approach in schools is g...

A total k-labeling is defined as a function g from the edge set to the first natural number ke and a function f from the vertex set to a non-negative even number up to 2kv, where k = max{ke, 2kv}. A vertex irregular reflexive k-labeling of the graph G is total k-labeling if wt(x) ¹ wt(x¢) for every two different vertices x and x¢ of G, where wt(x)...

The metaliteracy ability is a very important in today's life, especially to live in the disruptive technology era. Metaliteracy is an ability that goes beyond metacognition and technological literacy. However, the students' metalliteracy ability is still relatively low. One of the causes of the low ability is due to the learning model that has been...

This paper address the cryptographic keys management problem: how to generate the cryptographic keys and apply them to secure encryption. The purpose of this research was to study on utilizing graph labeling for generating stream-keys and implementing the keys for strengthening Vigenere encryption. To achieve this objective, the research was carrie...

Let $G$ is a connected graph with vertex set $V(G)$ and edge set $E(G)$. The side weights for $uv\in E(G) $ bijective function $f:V(G)\rightarrow\{1,2,\dots, |V(G)|\}$ and $ w(uv)= f(u)+f(v) $ . If each edge has a different weight, the function $f$ is called an antimagic edge point labeling. Is said to be a rainbow path, if a path $P$ on the graph...

Sausage is a food that is much favoured by the Indonesian people. Sausage belongs to a group of frozen food products that require cold storage. The weakness of sausages is to become stale when opened and exposed to the free air. It encourages sausage manufacturers to use preservatives in their products. A natural preservative that does not cause ne...

Dalam menyelesaikan persoalan matematika, terlebih yang mengintegrasikan permasalahan di kehidupan sehari hari diperlukan kemampuan metaliterasi siswa. Metaliterasi merupakan kerangka berpikir yang menyeluruh dan menjadi sumber referensi mandiri yang bersifat luas dibandingkan dengan jenis literasi lainnnya. Kemampuan metaliterasi siswa saat ini da...

The rainbow vertex connection was first introduced by krivelevich and yuster in 2009 which is an extension of the rainbow connection. Let graph $G =(V,E)$ is a connected graph. Rainbow vertex-connection is the assignment of color to the vertices of a graph $G$, if every vertex on graph $G$ is connected by a path that has interior vertices with diff...

Let a simple and connected graph $G=(V,E)$ with the vertex set $V(G)$ and the edge set E(G). If there is a mapping $f$: $V(G)$ $\rightarrow$ ${0,2,…,2k_v}$ and $f$: $E(G)$ $\rightarrow$ ${1,2,…,k_e}$ as a function of vertex and edge irregularities labeling with $k=max$ ${2k_v,k_e}$ for $k_v$ and $k_e$ natural numbers and the associated weight of ve...

All graph in this paper is simple and connected graph where $V(G)$ is vertex set and $E(G)$ is edge set. Let function $f : V(G)\longrightarrow \{0, 2,..., 2k_v\}$ as vertex labeling and a function $f: E(G)\longrightarrow \{1, 2,..., k_e\}$ as edge labeling where $k=max\{2k_v,k_e\}$ for $k_v,k_e$ are natural number. The weight of vertex $ u,v\in V(G...

Let be a finite collection of simple, nontrivial and undirected graphs. A graph is as antimagic total covering if there is bijectif function for every subgraph in which isomorfic to and the total weight, form arithmetic sequence , in which a,b are integers and n is a number of graph cover of which the result of total comb product operation. A antim...

Suppose the set W = {s1, s2,…, sk} is a subset of the vertex set V(G). The representation of a vertex v of G with respect to W as follows rm(v|W) = { d(v, s1), d(v, s2), … , d(v, sk)} where d(v, si),1 ≤ i ≤ k is the distance between the vertex v with the vertices of set W together with their multiplicities. The set W is called the m-local resolving...

The metaliteracy ability is a very important in today's life, especially to live in the disruptive technology era. Metaliteracy is an ability that goes beyond metacognition and technological literacy. However, the students' metalliteracy ability is still relatively low. One of the causes of the low ability is due to the learning model that has been...

Let $G=(V(G),E(G))$ is a graph connected non-trivial. \textit{Rainbow connection} is edge coloring on the graph defined as $f:E(G)\rightarrow \{1,2,...,r|r \in N\}$, for every two distinct vertices in $G$ have at least one \textit{rainbow path}. The graph $G$ says \textit{rainbow connected} if every two vertices are different in $G$ associated with...

In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \textbf{$l:V(G) \longrightarrow {\{1, 2, ..., k}\}$} is called vertex irregular k-labelling and \textbf{$w:V(G) \longrightarrow N$} where \textbf{$w(u) = \varSigma_{ v \in N(u)}l(v)$}, $w$ is called local irregularity vertex colori...

The ability of metaliteracy is very important in the industrial era 4.0. Metaliteracy is a comprehensive framework of thinking that goes beyond other literacies with the main literacy being information literacy. It is indicated that the metaliteracy of students is still low, it is because this literacy is still relatively new. The use of the IoT in...

For $k \geq 1$, in a graph $G=(V,E)$, a set of vertices $D$ is a distance $k$-dominating set of $G$, if any vertex in $V$ not in $D$ is at distance at most $k$ from some vertex in $D$. An ordered set of vertices $W=\{w_1,w_2,\ldots,w_r\}$ is a resolving set of $G$, if for any two distinct vertices $x$ and $y$ in $V\setminus W$, there exists $1\leq...

One needed in disruptive technology is metaliteracy. It refers to literacy covering any literacy achievements especially technology and information. Its main indicators are the abilities to produce, incorporate, use, share and collaborate. Thus, higher order thinking skill is required to access these indicators by implementing the research-based le...

This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V ( G ) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of g...

Let G = ( V, E ) be a simple finite connected and undirected graph with n vertices and m edges. The n vertices are assigned the colors through mapping c : V [ G ] → I ⁺ . An r -dynamic coloring is a proper k -coloring of a graph G such that each vertex of G receive colors in at least min{ deg ( υ ), r } different color classes. The minimum k such t...

We established new single-condition criteria for the oscillation of all solutions to a second-order half-linear advanced equation of the form ∆( φ ( ζ )(∆ x ( ζ )) ν ) + ρ ( ζ ) x ν ( ζ + η ) = 0; ζ ≥ ζ 0 under the conditions that ∑ s = ζ ∞ 1 ϕ 1 v ( s ) < ∞ . We derive new single-condition constraints for the oscillation of all unimprovable consta...

Let χ ( G ) be a chromatic number of proper coloring on G . For an injection f : V ( G ) → {0, 2, . . . ; 2 k υg } and f : E ( G ) → }1, 2, . . . , k e }, where k = max{ k e , 2k χ } for k υ , k e are natural number. The associated weight of a vertex u, υ ∈ V ( G ) under f is w ( u ) = f( u ) + ∑ uυ ∈E ( G )f( uυ ). The function f is called a local...

Let G ( V ( G ), E ( G )) be a connected, simple, and finite graph. Let f be a bijective function of labeling on graph G from the edge set E ( G ) to natural number up to the number of edges of G . A rainbow vertex antimagic labeling of graph G is a function f under the condition all internal vertices of a path u – υ , Ɐ u, υ ∈ V ( G ) have differe...

Nowadays, cryptosystems can be applied in several areas in life. One of them is in transaction data. In transaction data, a very strong cryptosystem is needed so that the transaction data is safe. Cryptosystems are better with a strong keystream. In this case, we use rainbow antimagic as a cryptosystem key to improve the robustness of the keystream...

Problem-solving can grow if students are trained to have metaliteracy. Metaliteracy is the ability to think that focuses on critical thinking skills and collaborative efforts. This study aims to determine the impact of the implementation of RBL-STEM to analyze the metaliteracy of students in solving rainbow antimagic coloring problems. The methods...

We examine that all graphs in this paper are limited, simple and connected. A graceful k -coloring of a graph is a proper vertex coloring f 1 : V ( G ) → {1, 2,…, k } where k ≥ 2 which induces a proper edge coloring f 2 : E ( G ) → {1, 2,…, k − 1} characterized by f 2 ( uυ ) = | f 1 ( u ) — f 2 ( υ )|. Nethermost k for which a graph G has a gracefu...

We use finite, connected, and undirected graph denoted by G . Let V ( G ) and E ( G ) be a vertex set and edge set respectively. A subset D of V ( G ) is an efficient dominating set of graph G if each vertex in G is either in D or adjoining to a vertex in D . A subset W of V ( G ) is a resolving set of G if any vertex in G is differently distinguis...

The purpose of this study is to develop rainbow antimagic coloring. This study is a combination of two notions, namely antimagic and rainbow concept. If every vertex of graph G is labeled with the antimagic labels and then edge weight of antimagic labels are used to assign a rainbow coloring. The minimum number of colors for a rainbow path to exist...

Let H be simple, non-isolated vertex, connected and directionless graphs with vertex set V ( H ), edge set E ( H ). With the use of c -coloring of graph H , using the formula c : υ ( H ) → S , where | S | = c , the colors of the adjacent vertex are different. A proper c-coloring of H is an r -dynamic coloring if it’s applied to every vertex υ ∈ V (...

Misal $G$ dan $K$ adalah graf sederhana, nontrivial dan graf tak berarah. Operasi \emph{total comb product} menghasilkan graf baru dengan mengoperasikan dua buah graf. Misalkan \emph{G} dan \emph{K} adalah graf terhubung dan \emph{v} $\in$ \emph{V(K}) dan \emph{e} $ \in $ \emph{E(K)}. Operasi \emph{total comb product} dari graf \emph{G} dan \emph{K...

Let G(V (G), E(G)) be a connected, undirected, and simple graph with vertex set V (G) and edge set E(G). For a bijective function f : V (G) → {1, 2, . . . , |V (G)|}, the associated weight of an edge uv ∈ E(G) under f is wf (uv) = f (u) + f (v). The function f is called an edge-antimagic vertex labeling if every edge has distinct weight. A path P i...

All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by for every . If G has a ant...

Let [Formula: see text] be a simple, finite, undirected, and connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bijection [Formula: see text] is label function [Formula: see text] if [Formula: see text] and for any two adjacent vertices [Formula: see text] and [Formula: see text], [Formula: see text] where [Form...

Let $G=(V(G),E(G))$ be a nontrivial connected graph. The edge coloring is defined as $c:E(G) \rightarrow \{1,2,...,k\}, k \in N$, with the condition that no adjacent edges have the same color. \emph{k}-color \emph{r}-dynamic is an edge coloring of \emph{k}-colors such that each edge in neighboring $E(G)$ is at least min $\{r,d( u)+d(v)-2\}$ has a d...

Graph coloring began to be developed into coloring dynamic. One of the developments of dynamic coloring is $r$-dynamic total coloring. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph. Total coloring is defined as $c:(V(G) \cup E(G))\rightarrow {1,2,...,k}, k \in N$, with condition two adjacent vertices and the edge that is adjacent to the...

All graph in this paper is a simple and connected graph. We define $l: V(G) \to \{ 1, 2, 3,...k\} $ is called vertex irregular k-labeling and $w: (G) \to N$ the weight function with $[\sum_{u \epsilon N} l(u) + l(v) ]$. A local irregularity inclusive coloring if every $u, v \epsilon E(G), w(u) \ne w(v) $ and $max (l) = min \{ max (l_i), l_i label f...

Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with edge coloring defined as $c:E(G) \rightarrow \{1,2,...,k\} ,k \in N$, with the condition that neighboring edges can be the same color. An original path is {\it rainbow path} if there are no two edges in the path of the same color. The graph $G$ is called rainbow connected if every two ve...

Let $G=(V, E)$ be a set of ordered set $W=\{W_1,W_2, W_3,...,W_k\}$ from the set of vertices in connected graph $G$. The metric dimension is the minimum cardinality of the resolving set on $G$. The representation of $v$ on $W$ is $k$ set. Vector $r(v|W)=(d(v, W_1), d(v, W_2), ...,$ $d(v, W_k))$ where $d(x, y)$ is the distance between the vertices $...

Let ${H_i}$ be a finite collection of simple, nontrivial and undirected graphs and let each $H_i$ have a fixed vertex $v_j$ called a terminal. The amalgamation $H_i$ as $v_j$ as a terminal is formed by taking all the $H_i$'s and identifying their terminal. When $H_i$ are all isomorphic graphs, for any positif integer $n$, we denote such amalgamatio...

This research aimed to describe the development process and results of the Construct 2 Android-based education math game on number pattern subjects to increase student's ICT literacy. This research employed the Research and Development method with a 4-D development model. The development model consisted of 4 stages: the Define stage, the Design sta...

Assume that G = (V;E) is an undirected and connected graph with vertex set V and edge set E. D is called a dominating set of the vertex in G such that for each vertex v 2 V one of: v 2 D or a neighbor u of v in D with u 2 D. While locating dominating set of G is a dominating set D of G when satisfy this condition: for every two vertices u; v 2 (V ...

There is a specific complexity in the use of IOT, especially in maintaining a secure data transaction. We need a good cryptosystem, since the best encryption key relays on the management cryptosystem. The biggest problem, then, is how to encrypt the plaintext into a ciphertext as hard as possible. We attempt to use the local super antimagic total f...

A function f with domain and range are respectively the edge set of graph G and natural number up to ke, and a function f with domain and range are respectively the vertex set of graph G and the even natural number up to 2kv are called a total k-labeling where k=max{ke,2kv}. The total k-labeling of graph G by the condition that every two different...

Innovative creative thinking skills play an important role in supporting students in solving mathematical concepts, especially simple multiplication operational problem with Jarimatika . The researchers applied mixed methods with a sequential explanatory design. Research subjects were 28 students in the experimental class and 26 students in the con...

Fractions are one of the mathematics topics that have been taught starting in grade two on elementary school. For kids, understanding a fraction is not so simple, especially in sorting fractions, ascending or descending. A fraction consists of two part numerator and denominator. A common technique frequently used in sorting some fractions is making...

Lack of insertion or understanding of local culture and traditions in classroom learning will cause students to appreciate the existing culture and grow in their environment. This research is a development research. The stages that has been through to make a valid, practical, and effective calculus learning tool are: 1) defining stage, 2) planning...

The HOTS (Higher-order thinking skill) is significantly important, especially in the twenty century. One of the indicators of HOTS is metacognition skill. This skill is related to how students can understand and control their learning styles and mechanisms. However, encouraging the rise of students’ metacognition skills is considered to be a challe...

Developing critical and collaborative thinking skills among learners was of significant importance in the 21st-century era. In this study, the researcher applied teaching and learning based on Research-Based Learning (RBL) to know the level of students critical thinking skill. The number of research samples was 30 students. This study used a triang...

Let G be a graph, then the dominator coloring of G is a proper coloring, in which every vertex of G dominates every vertex of at least one color class. The Total dominator coloring of graph is a proper coloring with extra property that every vertex in the graph properly dominates an entire color class. The total dominator chromatic number X d t ( G...

The set D ⊆ V ( G ) is called dominating set on graph G so that every vertex not in D is adjacent to at least one vertex in D . The set D t ⊆ V ( G ) is called total dominating set on graph G so that the vertex in D t are neighboring at least one dot in D t . The smallest cardinality of the total dominating set is referred to as total domination nu...

This research aimed to describing the metacognition skills of mathematical olympiad students’ in solving the national sciences olympiad problem on two-variables linear equation system material. The participants were four mathematical olympiad students at Banyuglugur–Situbondo. This research used qualitative descriptive research. Test and interview...

Dominating set is a set D of vertices of graph G ( V, E ) and every vertex u ∈ V ( G ) − D is adjacent to some vertex υ ∈ D . The set D is called independent set if no two vertices in D are adjacent. Independent domination number of G is the minimum cardinality of D and denoted by γ i ( G ). The metric representation of vertex υ in connected graph...

A rainbow antimagic coloring is one of new topics in graph theory. This topic is an expansion of rainbow coloring that is combined with antimagic labeling. The graphs are labeled with an antimagic labeling, and then the sum of vertex label have to obtain a rainbow coloring. The aim of the rainbow antimagic coloring research is to find the minimum n...

Let G be a connected, finite, and undirected graph. A vertex set D in G is an efficient dominating set of G if D is an independent set and for each point υ ∈ V ( G )- D is adjacent to precisely one vertex d ∈ D. The representation of points υ ∈ V ( G ) in respect of an ordered set W = { w 1 , w 2 ,…, w k } is the k –vector r ( υ | W ) = ( d ( υ , w...

A set of vertices D ⊆ V ( G ) is the dominating set of graph G if every vertex on graph G is dominated by dominators. The dominating set of D on graph G is a perfect if every point of a graph G is dominated by exactly one vertex on D . For each vertex υ ∈ V ( G ), the k -vector r ( υ | W ) is called the metric code or location W , where W = { w 1 ,...