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The purpose of this study was to describe students’ mathematical reasoning abilities, such as: drawing conclusions from a statement, doing mathematical manipulation, providing valid arguments and presenting mathematical statements, both verbally and in writing, in the form of pictures or graphs. This research used the descriptive qualitative method. The instruments used in this study were the main instrument (researchers) and the supporting instruments (tests and interviews). The test was given to 25 students of class XII SMA Muhammadiyah Surakarta Special Program (Muhammadiyah Surakarta Senior High School Special Program). The subjects of this study were eight students of class XII who were selected by purposive sampling technique. The results showed that students had good mathematical reasoning skills while doing mathematical manipulations and presenting mathematical statements verbally, in writing, or in pictures. Students did not show good mathematical reasoning skills when students have to draw conclusions from a statement and provide valid arguments. This is because students still do not master how to identify and determine the right strategy to solve problems, and the answers given by students were still not correct. In the future, teachers are expected to provide problems (questions) in various mathematical reasoning, so students are accustomed to working on problems with various levels of mathematical reasoning, and students’ mathematical skills can be better trained.

Assume that G(V,E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k. We call the function λ as a totally irregular total k-labeling if the set of weights of vertices and edges consists of different numbers. For any u ∈ V, we have a weight wt(u)=λ(u)+ ∑{uy ∈ E} λ(uy). Also, it is defined a weight wt(e)= λ(u)+ λ(uv) + λ(v) for each e=uv ∈ E. A minimum k used in k-total labeling λ is named as a total irregularity strength of G, symbolized by ts(G). We discuss results on ts of some caterpillar graphs in this paper. The results are ts(S{p,2,2,q}) = ⌈ (p+q-1)/2 ⌉ for p, q greater than or equal to 3, while ts(S{p,2,2,2,p}) = ⌈(2p-1)/2 ⌉, p ≥ 4.

In this research, we use the concept of a vertex irregular total k labeling and tvs(G). Specifically, we investigate tvs of generalized uniform cactus chain graphs with (n – 2)r pendant vertices an...

Let GV E (,) be a graph. Throughout this paper, we use the notions of edge irregular total k-labeling and total edge irregularity strength of G (tes (G)). We verify tes of general uniform cactus chain graphs 2 ( ) n C Cr n − having ( 2) n r − pendant vertices and length r. The result obtained is as follows: 2 (2 2) 2 3 (( ) n r n n r tes C C −   − + =   for n ≥ 6.

We focus on fuzzy graphs with crisp vertex and fuzzy edge sets. A concept of the fuzzy chromatic number of these graphs based on fuzzy independent vertex set is used in this paper. A modified algorithm called a fuzzy chromatic algorithm is developed to find the fuzzy chromatic number of union of fuzzy graphs. Running time and complexity of the algorithm are also analyzed. Furthermore, we investigate some properties of the fuzzy chromatic number of union of fuzzy graphs. Finally, an application of the fuzzy chromatic number to determine the number of phases of an integrated traffic light system is proposed. We get different phases with different degrees of safety.

Problem solving is significant skill in facing 21st century. Students have different levels of problem solving. The levels that explain individual abilities in solving mathematics problems are called as cognitive level. It consists of three levels; cognition, metacognition, and epistemic cognition. The cognitive level influences individual in understanding the problem and deciding the right strategies to solve it. The material used to obtain the data is three variables linear equation system, by involving two high ability students at the tenth grade from one of the state senior high schools in Pati. This research employs qualitative method, which the data are collected through task-based interview and time triangulation is applied to validate the data. The results reveal that at the cognition level, students with high ability have an understanding related to conceptual and procedural knowledge, but the ability of students in factual knowledge is low, especially in terminology skill; at the metacognition level, the students are able to write down each strategy in each method, but it is not detail; while at the epistemic cognition level, they are able to explain the weaknesses of a method, but they have not been able to provide a solution to overcome its weaknesses.

This research is motivated by the importance of problem solving skill for students in 21st century, whereas students' skill in solving mathematics problems is various in accordance their cognitive levels. Students’ cognitive levels in solving problems include; cognition; metacognition; and epistemic cognition. Cognitive level affects individual in understanding problem and deciding the right strategy to solve it. The purpose of this study is to describe cognitive levels of low-ability students. This study uses qualitative methods with task-based interviews. The material is three-variable linear equation system. The research subjects are two low-ability students at ten grade of State Senior High School in Pati Regency. The results show that the two subjects have weaknesses at each level, for example the two subjects are able to work on the given problems, but both subjects are unable to define equations, inequality, similarity, and dissimilarity correctly in the initial type of cognition level.

In this research, we examine total vertex irregularity strength (tvs) of tadpole chain graph Tr(4,1) with length r. We obtain that tvs (Tr(4, 1))=⌈4r+2/5⌉. Further, we construct algorithm to determine label of vertices, label of edges, weight of vertices, and the exact value of tvs of Tr(4, 1).

Let G be an undirected and simple graph with vertices set V(G) and edges set E(G). An edge irregular reflexive k-labeling f such that element edges labeled with integers number {1,2,…,ke} and vertices labeled with even integers {0,2,…,2kv}, k = max{ke, 2kv} of a graph G such that the weights for all edges are distinct. The weight of edge xy in G, symbolized by wt(xy) is defined as wt(xy) = f(x) + f(xy) + f(y). Reflexive edge strength is the minimum k for which the graph G has an edge irregular reflexive k-labeling, notated by res(G). In this paper we determine the exact values of the reflexive edge strength of banana tree graphs B2,n and B3,n.

We presume that G(V, E) is a simple, undirected, and connected graph. A function λ from V ∪ E to {1, 2,…, k} is named a totally irregular total k-labeling if the set of vertex-weights and the set of edge-weights of G consist of different values. The minimum integer k in such a way that G has a totally irregular total k-labeling is mentioned as total irregularity strength of G, denoted by ts(G). We investigate the total irregularity strength of the caterpillars that have an even number of internal vertices with degree three. The results are as follows: ts(Sn,3,3,…,3,︸tSn)=2n+(t−1)2 and ts(Sm−1,3,3,…,3,︸tSm)=2m+(t−1)2 for even number t.

Pneumonia is an infectious disease caused by microorganisms such as viruses, fungi and bacteria. This article focuses on pneumonia caused by bacteria Haemophilus influenzae type b (Hib). The purpose in this article is to formulate the susceptible vaccinated carrier infected recovered (SVCIR) model, apply the model for pneumonia in Indonesia, determine the pattern of its spread, and interpret the result of applying the model. The SVCIR model is a first order nonlinear differential equation system with the independent variable t and the dependent variables S, V, C, I and R. The SVCIR model was applied to pneumonia in Indonesia by the estimating the parameters values based on annual data for 2013–2018. Based on the application, it is known that there are still 2123586 cases of pneumonia in 2030. Therefore, based on the SVCIR model with initial values and parameters used, the target of Indonesia free of pneumonia in 2030 is estimated not to be reached and only reached in 2095. Therefore, simulation was carried out to reach Indonesia that free pneumonia by 2030. Based on the simulation, by increased vaccination rate is from α = 0.016940 to α = 2.158900 or the contact rate is decreased from β = 1.805109 to β = 0.057143 and simultaneously the vaccination rate is increased from α = 0.016940 to α = 0.033338 and decreased the contact rate from β = 1.805109 to β = 0.057706 while the other parameters have not changed the target for Indonesia to be free of pneumonia by 2030 can be achieved.

Let G be a connected graph with vertex set V(G) and egde set E(G). An edge irregular reflexive k-labeling is a function fe : E(G) → {1,2,…,ke} and a function fv : V(G) → {0,2,…, 2kv}, where k = max {ke, 2kv} of a graph G such that the weights for all edge are distinct. Under f labeling for edges and vertices, the weight of edge xy in G, denoted by wt(xy) is defined as wt(xy) = f(x) + f(xy) + f(y). The minimum k for which the graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, denoted by res(G). In this paper, we investigate the reflexive edge strength of tadpole graph Tm,n with m ≥ 3 and n = 1,2.

The conflict driven clause learning or CDCL is one of algorithm widely used in a lot of modern SAT solvers. It is because CDCL SAT solvers are so effective in practice, thanks to its non-chronological backjumping and conflict analysis. In this paper, we will discuss about the organization of CDCL solver for SAT solving and how it can be applied for satisfiability modulo theory. We also do experiment on hard-square constraint and found that the computation time using SMT solver follows an exponential function and the precomputation time is not affectedby the increase in the number of blanks.

Let G be an undirected and connected graph with vertex set V(G) and edge set E(G). An edge irregular reflexive k-labeling is a function fe : E(G) → {1, 2,…, ke} and a function fv : V(G) → {0,2,…,2kv}, where k = max {ke, 2kv} of a graph G such that the weights for all edge is distinct. Under f labeling for edges and vertices, the weight of edge xy in G, denoted by wt(xy) is defined as wt(xy) = f(x) + f(xy) + f(y). The minimum k for which the graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, denoted by res(G). This paper contains investigation of edge irregular reflexive k-labeling of umbrella graphs U3,n and U4,n.

One area of education which has not escaped efforts to improvethe Indonesian government is mathematics education. The Indonesian government must make good use of mathematics learning so that students can use the mathematical mindset to offset the pace of global competition. This research is an experimental research on the Process-Oriented Guided Inquiry Learning (POGIL) model on the ability of mathematical connections in terms of self-regulated learning. The design used in this study was a 2×3 factorial. The research sample was 179 students from 7th grade in three State Junior High Schools in Sukoharjo Regency, Central Java, Indonesia. The research sample consisted of an experimental group that subjected to the POGIL model and a control group that subjected to a direct learning model. This research instrument used was a written test and questionnaire. The data analysis technique used was a two-way ANOVA test with unbalanced cells and post hoc test. The results showed that: 1) the POGIL model produces better mathematical connection ability than the direct learning model, 2) Students with high category self-regulated learning have better mathematical connection ability than medium and low categories, and students with self-regulated learning the medium category have better mathematical connection ability than the low category.

This research aimed to determine the relationship between self-regulated learning with mathematical connection ability of students at State Junior High School. The method used in this research is survey method with the correlation technique. The research sample was 91 samples of State Junior High Schools in Sukoharjo Regency, Central Java, Indonesia, with heterogeneous abilities. The instruments used in this research were written tests of mathematical connection abilities on triangles and quadrilateral material, and a set of self-regulated learning questionnaire statements. Data analysis of mathematical connection ability and self-regulated learning in this research is Pearson correlation analysis. The results of the research data analysis showed a positive correlation between self-regulated learning and student’s mathematical connection ability. The contribution of self-regulated learning to students’ mathematical connection ability is 18.8%. Students have good self-regulated learning can foster a strong...

Let 𝐺 = (𝑉, 𝐸) be a connected and simple graph with vertex set 𝑉(𝐺) and edge set 𝐸(𝐺). A non inclusive distance vertex irregular labeling of a graph 𝐺 is a mapping of 𝜆 ∶ (𝑉, 𝐺) → {1, 2, … , 𝑘} such that the weights calculated for all vertices are distinct. The weight of a vertex 𝑣, under labeling 𝜆, denoted by 𝑤𝑡(𝑣), is defined as the sum of the label of all vertices adjacent to 𝑣 (distance 1 from 𝑣). A non inclusive distance vertex irregularity strength of graph 𝐺, denoted by 𝑑𝑖𝑠(𝐺), is the minimum value of the largest label 𝑘 over all such non inclusive distance vertex irregular labeling. In this research, we determined 𝑑𝑖𝑠(𝐺) from 𝑇𝑚,𝑛 graph with 𝑚 ≥ 3, 𝑚 odd, 𝑎𝑛𝑑 𝑛 ≥ 1 and 𝑃𝑛 ⊙ 𝑃𝑛 graph 𝑤𝑖𝑡ℎ 𝑛 ≥ 2 and 𝑛 even.

Mathematical connection skill is needed by students to connect mathematics theory and contextual problem solving. As state, in NCTM that the mathematical connections skill is one of the four competencies needed to face the industrial revolution 4.0. According to NCTM, there are three mathematical connection skills, namely modeling problems, applying obtained concepts and procedures also expanding mathematics ideas. The purpose of this study was to describe the class X student’s mathematical connection skill at Boyolali High School, Central Java in doing a contextual problem in one variable linear inequality. This research was a comparative descriptive study with qualitative methods involving 15 students from 5 schools as participants. The results showed that students’ mathematical connection skill is still low. We saw this from the indicators showed that the students were unable in modeling the contextual problems correctly, students were not able in applying the obtained the concepts and procedures also getting difficulty in expanding mathematics ideas.

Let G(V, E) be an undirected and simple graph with vertex set V and edge set E Define a k -labeling f on G such that the element belong to E are labeled with integers {1,2,…,ke } and the element belong to V are labeled with even integers {0,2,…,2kv }, where k = max{ke ,2kv }. A k -labeling f is mentioned as an edge irregular reflexive k -labeling if distinct edges have distinct weight. The weight of edge xy is denoted by wt(xy) and defined as wt(xy) = f (x) + f (xy) + f (y). A minimum k for which G has an edge irregular reflexive k -labeling is called reflexive edge strength of G and denoted by res(G). This paper contains investigation of edge irregular reflexive k -labeling for corona of path and other graphs and determination of their reflexive edge strengths.

Throughout this paper, we use the concept of fuzzy chromatic number (FCN) of fuzzy graphs based on δ-fuzzy independent vertex sets with δ ∈ [0,1] published in 2015. In this paper, we construct two type algorithms to determine fuzzy chromatic number of cartesian product and join of fuzzy graphs. The first type algorithm is constructed to find FCN of specific fuzzy graphs based on formulas in the theorems. The second type algorithm is designed to establish FCN of cartesian product and join of any fuzzy graphs based on the concepts of the cartesian product and join of fuzzy graphs and fuzzy chromatic algorithm. Experimental results of the algorithms are also discussed.

Problem-solving is one of the 21st century skills that belief is important for students to learn. Mathematics problem solving is the mathematical process that enables to use the skills in a wide variety of situations. The problems mean a situation that presents a challenge, offers an opportunity or anxiety and to solve mathematical problems. Every student has different characteristics and attitude in order to face adversity that called mathematical resilience. This research aims to describe the mathematics problem-solving ability of students of grade VIII SMP Negeri in Sragen region and found the patterns of mathematical problem-solving abilities that were analyzed based on students’ mathematical resilience. The method was used in this research is descriptive quantitative research with 153 students as the samples. Data was collected using questionnaire and written test. The result of the research gave an overview that mathematical problem-solving ability of students having the high resilience level of mathematics can deal with and be able to overcome obstacles and negative situations that related in the problemsolving process because of they can successfully coach themselves. Students which are given non-routine mathematical problem, showed differences students' mathematics problem solving based on levels of mathematical resilience.

We study a fuzzy graph with a crisp vertex set and a fuzzy edge set. In this paper, an approach to determine fuzzy chromatic number of fuzzy graphs based on partitioning the vertex set into fuzzy independent vertex sets has been used. By using this method, we investigate a generalization of chromatic number of join crisp graphs into fuzzy chromatic number of join fuzzy graphs and prove an associated property. Further, an apllication of fuzzy chromatic number in a traffic light system is proposed.

The purpose of this research is to know the motivation of mathematics learning in high school students of 10th grade. Data collection method is done in the form of survey conducted in Purbalingga. The instrument used is a questionnaire of motivation to learn math. Interview method is also done to get additional data which is used as supporting data in conducting analysis of data obtained previously. The result of the survey shows that the students of both schools have a high motivation to learn math with an average of 3.39. Based on the results of the analysis, a lot of the students who have high learning motivation on math dissatisfied with the value of daily tests and examinations with an average index of 2.31. It shows that high learning motivation is not enough to get a satisfactory value. The statement was corroborated by points on the understanding of mathematical material that was only able to obtain an average index of 2.56. Based on the results of interviews from 3 students, they wanted to use a good learning media that had three characteristic, that was a learning media that taught students not to give up easily, that was able to bring out a sense of pleasure, and that was challenging. Therefore, beside high learning motivation, understanding of mathematics materials supported by the use of good learning media is also required.