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All Journal International Journal of Electrical and Computer Engineering CAUCHY: Jurnal Matematika Murni dan Aplikasi Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding Jurnal Matematika: MANTIK Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Indonesian Journal of Combinatorics CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Dedication : Jurnal Pengabdian Masyarakat
Ika Hesti Agustin, Ika Hesti
Department Of Mathematics, University Of Jember, Indonesia.
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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On The Local Metric Dimension of Line Graph of Special Graph Marsidi, Marsidi; Dafik, Dafik; Hesti Agustin, Ika; Alfarisi, Ridho
CAUCHY Vol 4, No 3 (2016): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (917.503 KB) | DOI: 10.18860/ca.v4i3.3694

Abstract

Let G be a simple, nontrivial, and connected graph.  is a representation of an ordered set of k distinct vertices in a nontrivial connected graph G. The metric code of a vertex v, where , the ordered  of k-vector is representations of v with respect to W, where  is the distance between the vertices v and wi for 1≤ i ≤k.  Furthermore, the set W is called a local resolving set of G if  for every pair u,v of adjacent vertices of G. The local metric dimension ldim(G) is minimum cardinality of W. The local metric dimension exists for every nontrivial connected graph G. In this paper, we study the local metric dimension of line graph of special graphs , namely path, cycle, generalized star, and wheel. The line graph L(G) of a graph G has a vertex for each edge of G, and two vertices in L(G) are adjacent if and only if the corresponding edges in G have a vertex in common.
On The Metric Dimension of Some Operation Graphs Marsidi, Marsidi; Agustin, Ika Hesti; Dafik, Dafik; Alfarisi, Ridho; Siswono, Hendrik
CAUCHY Vol 5, No 3 (2018): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (782.001 KB) | DOI: 10.18860/ca.v5i3.5331

Abstract

Let  be a simple, finite, and connected graph. An ordered set of vertices of a nontrivial connected graph  is  and the -vector  represent vertex  that respect to , where  and  is the distance between vertex  and  for . The set  called a resolving set for  if different vertex of  have different representations that respect to . The minimum of cardinality of resolving set of G is the metric dimension of , denoted by . In this paper, we give the local metric dimension of some operation graphs such as joint graph , amalgamation of parachute, amalgamation of fan, and .
On the Local Adjacency Metric Dimension of Generalized Petersen Graphs Marsidi, Marsidi; Dafik, Dafik; Agustin, Ika Hesti; Alfarisi, Ridho
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i1.6487

Abstract

The local adjacency metric dimension is one of graph topic. Suppose there are three neighboring vertex , ,  in path . Path  is called local if  where each has representation: a is not equals  and  may equals to . Let’s say, .  For an order set of vertices , the adjacency representation of  with respect to  is the ordered -tuple , where  represents the adjacency distance . The distance  defined by 0 if , 1 if  adjacent with , and 2 if  does not adjacent with . The set  is a local adjacency resolving set of  if for every two distinct vertices ,  and  adjacent with y then . A minimum local adjacency resolving set in  is called local adjacency metric basis. The cardinality of vertices in the basis is a local adjacency metric dimension of , denoted by . Next, we investigate the local adjacency metric dimension of generalized petersen graph.
Modification of Chaos Game with Rotation Variation on a Square Purnomo, Kosala Dwidja; Larasati, Indry; Agustin, Ika Hesti; Ubaidillah, Firdaus
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i1.6936

Abstract

Chaos game is a game of drawing a number of points in a geometric shape using certain rules that are repeated iteratively. Using those rules, a number of points generated and form some pattern. The original chaos game that apply to three vertices yields Sierpinski triangle pattern. Chaos game can be modified by varying a number of rules, such as compression ratio, vertices location, rotation, and many others. In previous studies, modification of chaos games rules have been made on triangles, pentagons, and -facets. Modifications also made in the rule of random or non-random, vertex choosing, and so forth. In this paper we will discuss the chaos game of quadrilateral that are rotated by using an affine transformation with a predetermined compression ratio. Affine transformation is a transformation that uses a matrix to calculate the position of a new object. The compression ratio r used here is 2. It means that the distance of the formation point is  of the fulcrum, that is  = 1/2. Variations of rotation on a square or a quadrilateral in chaos game are done by using several modifications to random and non-random rules with positive and negative angle variations. Finally, results of the formation points in chaos game will be analyzed whether they form a fractal object or not.
On the Domination Number of Some Families of Special Graphs Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

A domination in graphs is part of graph theory which has many applications. Its application includes the morphological analysis, computer network communication, social network theory, CCTV installation, and many others. A set $D$ of vertices of a simple graph $G$, that is a graph without loops and multiple edges, is called a dominating set if every vertex $u\in V(G)-D$ is adjacent to some vertex $v\in D$. The domination number of a graph  $G$, denoted by $\gamma(G)$, is the order of a smallest  dominating set of $G$. A dominating set $D$ with $|D|=\gamma(G)$ is called a minimum dominating set, see Haynes and Henning \cite{Hay1} . This research aims to find the domination number of some families of special graphs, namely Spider Web graph $Wb_{n}$, Helmet graph $H_{n,m}$, Parachute graph $Pc_{n}$, and any regular graph. The results shows that the resulting domination numbers meet the lower bound of an obtained lower bound $\gamma(G)$ of any graphs.
Pelabelan Total Super $(a,d)$-sisi Antimagic pada Graf Semi Parasut $SP_{2n-1}$ Aprilia, Karinda Rizqy; Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

Misalkan terdapat graf $G = (V,E)$. Suatu pemetaan bijeksi $g$ dari $V(G)\cup E(G)$ ke \{1,2,...,$|V(G)|$+$|E(G)|$\} dikatakan $pelabelan$ $total$ (a,d)-$sisi$ $antimagic$ di $G$, jika himpunan bobot sisi $W(x,y) = \{w(xy)|w(xy)=g(x)+g(y)+g(xy)\}$, $\forall$ $xy$ $\in$ $E(G)$ dapat dinyatakan sebagai barisan aritmatika dengan suku awal $a$ dan beda $d$. Pelabelan total $(a,d)$-sisi antimagic dikatakan $pelabelan$ $total$ $(a,d)-sisi$ $antimagic$ $super$ jika $g(V(G))=\{1,2,...,|V(G)|\}$. Pada makalah ini akan dikaji kembali tentang pelabelan total $(a,d)$- sisi antimagic pada graf semi parasut $SP_{2n-1}$ dengan $n \geq 2$.
Pelabelan Total Supaer $(a,d)$-Sisi Antimagic Pada Graf Daun Yunika, Sih Muhni; Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

Misalkan $G$ adalah graf  dengan himpunan titik $V(G)$ dan himpunan sisi $E(G)$. Suatu pemetaaan bijektif  $g$ dari $V(G)\bigcup E(G)$ ke $\{1,2,...,|V(G)|+E|(G)|\}$ dikatakan pelabelan total ($a,d$)-sisi antimagic di $G$, jika himpunan bobot sisi $W(xy)=\{w(xy)|x(xy)=g(x)+g(y)+g(xy),\forall xy \in E(G)$\}, dapat dinyatakan sebagai barisan aritmatika dengan suku awal $a$ dan beda $d$. Dikatakan sebagai pelabelan total ($a,d$)-sisi antimagic super jika $g(V(G))=\{1,2,...,|V(G)|\}$. Dalam penelitian ini akan dikaji tentang super  ($a,d$)-sisi antimagic pelabelan total pada graf daun, $n\geq 1$ dan $d\in \{0, 2\}$. Fokus pengkajian ini adalah pembentukan pola super ($a,d$)-sisi antimagic pelabelan total pada graf daun dengan $n\geq 1$.}
Graf-Graf Khusus dan Bilangan Dominasinya Muharromah, Agustina; Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

merupakan himpunan titik yang mendominasi titik-titik yang bertetangga dan seminimal mungkin. Himpunan $D \subseteq V(G)$ adalah \emph{dominating set} dari titik jika setiap titik di $V(G)$ bertetangga dengan sebuah titik di $D$. \emph{Domination number} $\gamma(G)$ adalah kardinalitas terkecil dari sebuah \emph{dominating set}. Nilai dari \emph{domination number} selalu $\gamma(G) \subseteq V(G)$. Penelitian ini mengembangkan \emph{dominating set} pada beberapa graf khusus diantaranya adalah graf Shackel $(S_{m},n)$, graf $C_n \odot (P_{4}+\overline{K}_{1})$, graf join $C_n+P_n$, graf Lobster $L_{i,j,k}$, dan graf Triangular Ladder $L_n$. Hasil dari penelitian ini adalah beberapa teorema yang menyatakan kardinalitas minimal \emph{dominating set}.}
Pewarnaan Titik Pada Operasi Graf Sikel Harsya, Alfian Yulia; Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

Pewarnaan titik adalah memberikan warna pada titik - titik graf  sehingga setiap dua titik yang bertetangga ($adjacent$) mempunyai warna yang berbeda. Warna-warna yang digunakan untuk mewarnai suatu graf dinyatakan  dengan 1, 2, 3, …, n, sehingga $\chi(G)$ $\leq$  $V(G)$. Operasi graf adalah beberapa cara untuk memperoleh graf baru dengan melakukan suatu operasi terhadap dua graf. Adapun macam -macam pengoperasian graf yaitu operasi $Joint$ $(G + H)$,\emph{Cartesian Product} $(G \Box H)$, \emph{Crown Product } $(G \odot H)$, \emph{Tensor Product } $(G \otimes H )$, \emph{Composition } $(G[F])$, \emph{Shackel}, dan \emph{Amalgamation}. Graf sikel $(cycle)$ merupakan graf sederhana yang setiap titiknya berderajat dua yang dilambangkan dengan $C_n$. Sedangkan graf lintasan $(path)$ ialah graf dengan barisan berselang-seling antara titik dan sisi yang berbentuk $v_0 , e_1 , v_1 , e_2 , v_2 ,..., v_{n-1} , e_n , v_n$ yang dilambangkan dengan $P_n$. Tujuan dari penelitian ini adalah menentukan operasi graf sikel dengan graf lintasan. Penelitian ini menghasilkan bilangan kromatik dan fungsi pewarnaan titik pada graf ($P_2 \otimes C_n$), $shack$($P_2 \otimes C_5$, n), ($P_3 \odot C_n$), ($P_n[C_3]$), dan $amal$($(P_2 \Box C_5) + P_2, v=1, n$).}
Super (a,d)-H Antimagic Total Covering Pada Graf Triangular Ladder Jamil, Nur Asia; Agustin, Ika Hesti; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

Pelabelan selimut ({\it a,d})-$\mathcal{H}$ antimagic pada graf $G$ adalah sebuah fungsi bijektif $\xi : V(G) \cup E(G) \rightarrow \{1,2,...,|V(G)|+|E(G)|\}$ sehingga semua subgraf $H'$ yang isomorfik dengan $H$ memiliki bobot subgraf $w(H')$=\-$\sum_{v\epsilon\- V(H')}\xi (v)$+$\sum_{e\epsilon E(H')}\xi (e)$ yang merupakan deret aritmatika $a,a+d,a+2d,...,a+(t-1)d$ dengan $a$ dan $d$ adalah bilangan bulat positif dan $m$ adalah jumlah subgraf dari $G$ yang isomorfik dengan $H$. Graf $G$ dikatakan sebuah graf super $\mathcal{H}$-antimagic jika $f(v)=\{1,2,...,|V|\}$ dengan $w(f)$ adalah sebuah jumlahan super antimagic. Tujuan dari penelitian ini adalah untuk menentukan pelabelan selimut super $(a,d)$-$C_3$-antimagic pada graf triangular ladder $d$ $\epsilon$ $\{0,1,2,3,4\}$. Penelitian ini menghasilkan 5 teorema yang menentukan suku awal {\it a} dan nilai beda {\it d} pelabelan selimut super ({\it a,d})-$\mathcal{H}$-antimagic pada graf triangular ladder.}
Co-Authors A. Y. Harsya Agustina Muharromah, Agustina Alfian Futuhul Hadi Alfian Yulia Harsya, Alfian Yulia Antonius Cahya Prihandoko Arika Indah Kriatiana Cangul, Ismail Naci D. Dafik Dafik Dafik Dwi Agustin Retnowardani Eric Dwi Putra Firdaus Ubaidillah, Firdaus Firdausiyah, Iftitahul Gembong A. W. Hani'ah Zakin Herninda Lucky Oktaviana Ida Ariska Ika Nur Maylisa Imro’atun Rofikah Ismail Naci Cangul Jannah, Excelsa Suli Wildhatul Karinda Rizqy Aprilia, Karinda Rizqy Kiki Kurdianto Kosala Dwidja Purnomo Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Larasati, Indry Lusia Herni Sullystiawati Mardiyah, Fitriyatul Marsidi Marsidi Marsidi Marsidi Md. Saidur Rahman Mohanapriya, N. Mursyidah, Indah Lutfiyatul N. Mohanapriya N. Mohanapriya Novian Nur Fatihah Nur Asia Jamil, Nur Asia Nuraeni Mauliddatul Fikria Prihandini, Rafiantika Megahnia Putri Rizky H.P, Putri Rizky Qonita Ilmi Awalin R. Sunder R. Sunder Rafiantika Megahnia Prihandini Reyka Bella Desvandai Ridho Alfarisi, Ridho Riza Nurfadila Robiatul Adawiyah Rosita, Merlinda S Slamin Sherly Citra Wuni, Sherly Citra Sih Muhni Yunika, Sih Muhni Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Sulisawati, Dwi Noviani Ukas Alif Fuadi Viqedina Rizky Noviyanti Yessy Eki Fajar Reksi