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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 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 Decision Sciences, Operations Research & Management Education Electrical & Electronics Engineering Mathematics Other

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Journal : CAUCHY

 1 
A Super (A,D)-Bm-Antimagic Total Covering of Ageneralized Amalgamation of Fan Graphs Agustin, Ika Hesti; Dafik, Dafik; Latifah, Siti; Prihandini, Rafiantika Megahnia
CAUCHY Vol 4, No 4 (2017): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (630.746 KB) | DOI: 10.18860/ca.v4i4.3758

Abstract

All graph in this paper are finite, simple and undirected. Let G, H be two graphs. A graph G is said to be an (a,d)-H-antimagic total graph if there exist a bijective function  such that for all subgraphs H’ isomorphic to H, the total H-weights form an arithmetic progression  where a, d 0 are integers and m is the number of all subgraphs H’ 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 will study a super (a, d)-Bm-antimagicness of a connected and disconnected generalized amalgamation of fan graphs on which a path is a terminal.
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 Rainbow Vertex Antimagic Coloring of Graphs: A New Notion Marsidi, Marsidi; Agustin, Ika Hesti; Dafik, Dafik; Kurniawati, Elsa Yuli
CAUCHY Vol 7, No 1 (2021): 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.v7i1.12796

Abstract

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 antimagic rainbow edge labeling, then  is a antimagic rainbow vertex connection, where the every vertex is assigned with the color . The antimagic rainbow vertex connection number of , denoted by , is the minimum colors taken over all rainbow vertex connection induced by antimagic rainbow edge labeling of . In this paper, we determined the exact value of the antimagic rainbow vertex connection number of path ( ), wheel ( ), friendship ( ), and fan ( ).
The Distance Irregular Reflexive k-Labeling of Graphs Ika Hesti Agustin; Dafik Dafik; N. Mohanapriya; Marsidi Marsidi; Ismail Naci Cangul
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.19747

Abstract

A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive strength of some connected graphs, namely path, star, and friendship graph.
Co-Authors A. Y. Harsya Agustina Muharromah, Agustina Alfian Yulia Harsya, Alfian Yulia Arika Indah Kriatiana D. Dafik Dafik Dafik Dwi Agustin Retnowardani Firdaus Ubaidillah, Firdaus Gembong A. W. Hani'ah Zakin Herninda Lucky Oktaviana Ida Ariska Imro’atun Rofikah Ismail Naci Cangul Karinda Rizqy Aprilia, Karinda Rizqy Kiki Kurdianto Kosala Dwidja Purnomo Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Larasati, Indry Marsidi Marsidi N. Mohanapriya Novian Nur Fatihah Nur Asia Jamil, Nur Asia Nuraeni Mauliddatul Fikria Prihandini, Rafiantika Megahnia Putri Rizky H.P, Putri Rizky Rafiantika Megahnia Prihandini Reyka Bella Desvandai Ridho Alfarisi, Ridho Riza Nurfadila S Slamin Sherly Citra Wuni, Sherly Citra Sih Muhni Yunika, Sih Muhni Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Ukas Alif Fuadi Viqedina Rizky Noviyanti Yessy Eki Fajar Reksi