Viqedina Rizky Noviyanti, Kusbudiono Kusbudiono, I. Agustin, D. Dafik
{"title":"Pewarnaan Sisi r-Dinamis pada Graf Khusus dan Graf Operasi Sakel","authors":"Viqedina Rizky Noviyanti, Kusbudiono Kusbudiono, I. Agustin, D. Dafik","doi":"10.25037/cgantjma.v2i1.47","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.47","url":null,"abstract":"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 different color. The dynamic emph{r}-edge coloring is defined as a mapping of $c$ from $E(G)$ such that $|c(N(uv))|$ = min${r,d(u)+d(v)- 2}$, where $N(uv)$ is the neighbor of $uv$ and $c(N(uv))$ is the color used by the neighboring side of $uv$. The minimum value of $k$ so that the graph $G$ satisfies the emph{k}-coloring emph{r}-dynamic edges is called the dynamic emph{r}-edge chromatic number. 1-dynamic chromatic number is denoted by $lambda(G)$, 2-dynamic chromatic number is denoted by $lambda_d(G)$ and for dynamic emph{r}-chromatic number is denoted by $lambda_r(G)$. The graphs that used in this study are graph $TL_n$, $TCL_n$ and the switch operation graph $shack(H_{2,2},v,n)$. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128932396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Desi Febriani Putri, D. Dafik, Kusbudiono Kusbudiono
{"title":"Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi","authors":"Desi Febriani Putri, D. Dafik, Kusbudiono Kusbudiono","doi":"10.25037/cgantjma.v2i1.51","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.51","url":null,"abstract":"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 vertex must have a different color. $r$-dynamic total coloring defined as the mapping of the function $c$ from the set of vertices and edges $(V(G)cup E(G))$ such that for every vertex $v in V(G)$ satisfy $|c(N(v))| = min{[r,d(v)+|N(v)|]}$, and for each edge $e=uv in E(G)$ satisfy $|c(N(e))| = min{[r,d(u)+d(v)]}$. The minimal $k$ of color is called $r$-dynamic total chromatic number denoted by $chi^{primeprime}(G)$. The $1$-dynamic total chromatic number is denoted by $chi^{primeprime}(G)$, chromatic number $2$-dynamic denoted with $chi^{primeprime}_d(G)$ and $r$-dynamic chromatic number denoted by $chi^{primeprime}_r(G)$. The graph that used in this research are path graph, $shackle$ of book graph $(shack(B_2,v,n)$ and emph{generalized shackle} of graph emph{friendship} $gshack({bf F}_4,e,n)$. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121478991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
U. A. Anwar, A. I. Kristiana, Arif Fatahillah, D. Dafik, R. Alfarisi
{"title":"Pewarnaan Ketakteraturan Lokal Inklusif pada Keluarga Graf Pohon Tree","authors":"U. A. Anwar, A. I. Kristiana, Arif Fatahillah, D. Dafik, R. Alfarisi","doi":"10.25037/cgantjma.v2i1.49","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.49","url":null,"abstract":"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 $max (l) = min { max (l_i), l_i label function}$. The chromatic number of local irregularity inclusive coloring of $G$ denoted by $chi_{lis}^{i}$, is the minimum cardinality of local irregularity inclusive coloring. We study about the local irregularity inclusive coloring of some family tree graph and we have found the exact value of their chromatic number. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131068262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wahyu Nikmatus Sholihah, D. Dafik, Kusbudiono Kusbudiono
{"title":"Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf","authors":"Wahyu Nikmatus Sholihah, D. Dafik, Kusbudiono Kusbudiono","doi":"10.25037/cgantjma.v2i1.48","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.48","url":null,"abstract":"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 $x$ and $y$. This study aims to determine the value of the metric dimensions and dimension of {it non-isolated resolving set} on the wheel graph $(W_n)$. Results of this study shows that for $n geq 7$, the value of the metric dimension and {it non-isolated resolving set} wheel graph $(W_n)$ is $dim(W_n)=lfloor frac{n-1}{2} rfloor$ and $nr(W_n)=lfloor frac{n+1}{2}rfloor$. The first step is to determine the cardinality vertices and edges on the wheel graph, then determine $W$, with $W$ is the resolving set $G$ if {it vertices} $G$ has a different representation. Next determine {it non-isolated resolving set}, where $W$ on the wheel graph must have different representations of $W$ and all $x$ elements $W$ is connected in $W$. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123016269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Konstruksi Rak Penataan Gelas Air Minum Menggunakan Hasil Deformasi Benda-Benda Geometri dan Kurva Bezier","authors":"Hikmah Ardiantika Sari, Bagus Juliyanto, Firdaus Ubaidillah","doi":"10.25037/cgantjma.v2i1.54","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.54","url":null,"abstract":"Drinking water glass shelves are used as containers that can hold drinking water with a growing model. Drinking water glass shelves is made using thecniques which produced from deformation of geometric objects and Bezier curves. This research aims to made produces procedures for designing buffers, main shelves and more varied reliefs with one axis and three modeling axes. This research method divided into several stages. First, construct some basic objects as constituent components of drinking water glass shelves from deformation of octagonal, tube, beams, and the ball. Second, set some basic objects of the component of drinking water glass shelves two types of modeling axis. Third, arrange program using Maple 13. The results of this research obtained the procedure for designing various forms of constituent components of drinking water glass shelves from the basic object of a octagonal, tube, beams, and the ball. Furthermore, the procedure for assembling the components of drinking water glass from the first procedure result on two types of modeling axis. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127693760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hani'ah Zakin, I. Agustin, Kusbudiono Kusbudiono, D. Dafik
{"title":"Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext","authors":"Hani'ah Zakin, I. Agustin, Kusbudiono Kusbudiono, D. Dafik","doi":"10.25037/cgantjma.v2i1.52","DOIUrl":"https://doi.org/10.25037/cgantjma.v2i1.52","url":null,"abstract":"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 amalgamation by $G={rm Amal}(H,v,n)$, where $n$ denotes the number of copies of $H$. The graph $G$ is said to be an $(a, d)$-$H$-antimagic total graph if there exist a bijective function $f: V(G) cup E(G) rightarrow {1, 2,dots ,|V (G)| + |E(G)|}$ such that for all subgraphs isomorphic to $H$, the total $H$-weights $w(H)= sum_{vin V(H)}f(v)+sum_{ein E(H)}f(e)$ form an arithmetic sequence ${a, a + d, a +2d,...,a+(t - 1)d}$, where $a$ and $d$ are positive integers and $t$ is the number of all subgraphs isomorphic to $H$. An $(a,d)$-$H$-antimagic total labeling $f$ is called super if the smallest labels appear in the vertices. In this paper, we study a super $(a, d)$-$H$ antimagic total labeling of $G={rm Amal}(H,v,n)$ and its disjoint union when $H$ is a complete graph. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121056943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Adelia Putri Liowardani, D. Dafik, Arif Fatahillah
{"title":"Pewarnaan Titik r-Dinamis pada Graf Hasil Operasi Edge Corona","authors":"Adelia Putri Liowardani, D. Dafik, Arif Fatahillah","doi":"10.25037/cgantjma.v1i2.42","DOIUrl":"https://doi.org/10.25037/cgantjma.v1i2.42","url":null,"abstract":"This research is a development of research on $r$-dynamic vertex coloring on simple, connected, and undirected graphs. The $r$dynamic vertex coloring on the graph $G$ is the $r$ point coloring of the $r$ graph so that the vertices of degree two on the $G$ graph have at least two different color neighbors. The $r$-dynamic vertex coloring is satisfied if it meets the conditions for $forall v in V(G)$, $|c(N(v))|$ $geq$ min${r,d(v)}$. The chromatic number for the $r$-dynamic vertex coloring of the graph $G$ is denoted as $chi_r(G)$. In this study, we discuss the $r$-dynamic vertex coloring on the graph resulting from the emph{edge corona} operation on a path graph with a complete graph, a star graph, and a sweep graph. It is denoted that the result of the operation of emph{edge corona} graph $G$ and graph $H$ is $G diamond H$. In this study, the results of the $r$-dynamic vertex coloring are described in the operation graph $P_n diamond K_m$, $P_n diamond S_m$, $P_n diamond P_m$, and $P_n diamond B_{(m,k)} ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123140381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Resolving Domination Number pada Keluarga Graf Buku","authors":"Quthrotul Aini Fuidah, D. Dafik, E. R. Albirri","doi":"10.25037/cgantjma.v1i2.44","DOIUrl":"https://doi.org/10.25037/cgantjma.v1i2.44","url":null,"abstract":"All graph in this paper are members of family of book graph. Let $G$ is a connnected graph, and let $W = {w_1,w_2,...,w_i}$ a set of vertices which is dominating the other vertices which are not element of $W$, and the elements of $W$ has a different representations, so $W$ is called resolving dominating set. The minimum cardinality of resolving dominating set is called resolving domination number, denoted by $gamma_r(G)$. In this paper we obtain the exact values of resolving dominating for family of book graph. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123951203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis Creative Thinking Pattern on X Sains 2 at SMAN 2 Jember to Solving Open Ended Problem of Space and Shape","authors":"E. Y. Kurniawati, D. Dafik, A. Fatahillah","doi":"10.25037/cgantjma.v1i2.46","DOIUrl":"https://doi.org/10.25037/cgantjma.v1i2.46","url":null,"abstract":"Math learning to train people to think critically, creatively, logical, analytical and systematic. In reality, mathematics is often regarded as the science that emphasizes logical thinking with a unique solution and certainly, so that students do not have the flexibility to develop creative ideas. The condition causes low creativity of students in learning mathematics. Curriculum 2006 stated that creative thinking skills needed to master the science of the future, given that today's science and technology is developing very rapidly cite{BSNP}. Thus, the ability to think creatively is important to develop. This study describes the rate and the process of creative thinking class X IPA 2 SMA Negeri 2 Jember, in solving open ended problems. Instruments used in this research is to test the ability to think creatively package A and package B, questionnaires and interview guidelines. Of the 36 students of class X IPA 2 SMA Negeri 2 Jember included TBK 0 (not creative) as much as two students (5.56%), TBK 1 (less creative) as many as twenty students (55.56%), TBK 2 (enough creative) thirteen students (36.1%), TBK 3 (creative) only one student (2.78%) and no students were able to achieve TBK 4 (very creative). Because there are only four levels of creative thinking then taken four students as research subjects who identified the creative thinking process. Students TBK 3 very fulfilling to aspects of fluency and flexibility aspects, but for the novelty aspect is still lacking. Students TBK 2 only meet the flexibility aspect alone. Students TBK 1 which fulfills the eloquence alone. Students who do not meet the TBK 0 fluency aspect, the aspect of flexibility and novelty aspect. ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129372956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pengembangan Affine Chiper dalam Pelabelan Super Antiajaib Graf Buku Bersusun Menggunakan Pemrograman Matlab","authors":"Vutikatul Nur Rohmah, D. Dafik, Arif Fatahillah","doi":"10.25037/cgantjma.v1i2.41","DOIUrl":"https://doi.org/10.25037/cgantjma.v1i2.41","url":null,"abstract":"Super $(a, d)-mathcal{H}-$ antimagic total covering labeling on a graph $G=(V,E)$ is total labelling $lambda$ on $V(G)UE(G)$ to set integers ${1,2,3,..., |V(G)UE(G)|}$ form an arithmetic sequence ${a, a+d, a+2d, . . .,a+(s-1)d}$ where $a, d$ are positive integer with $a$ is firt integer, $d$ is different, and $s$ is sum of covering. This research purposes to determine cardinality of vertex, cardinality of edge, upper limit of difference value, difference value from shackle of stacked book graph.The first step is determine cardinality of vertex and cardinality of edge on shackle of stacked book graph. Then determine upperlimit if difference value and the partition from labeling on shackle of stacked book graph. So that be produced super $(a, d)-mathcal{H}-$antimagic total covering labeling on shackle of stacked book ","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130220407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}