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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal ORTOPEDAGOGIA Jurnal Matematika: MANTIK Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika JPM : Jurnal Pendidikan Matematika Dedication : Jurnal Pengabdian Masyarakat PRISMATIKA: Jurnal Pendidikan dan Riset Matematika Cartesian: Jurnal Pendidikan Matematika Dedication : Jurnal Pengabdian Masyarakat Jurnal Manajemen, Ekonomi, Hukum, Kewirausahaan, Kesehatan, Pendidikan dan Informatika (MANEKIN) Noumerico: Journal of Technology in Mathematics Education
Marsidi Marsidi
Department Of Mathematics Education, University Of PGRI Argopuro Jember, Indonesia
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Economics, Econometrics & Finance Education Energy Law, Crime, Criminology & Criminal Justice Mathematics Social Sciences Other

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Journal : CAUCHY: Jurnal Matematika Murni dan Aplikasi

 1 
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.
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 Akmal Firdaus, Radika Akmala Dewi, Nur Aldiyanto, Muhammad Aris Noval, Muhammad Asrorul Mais Aswar Anas Aulia Fajar, Mohammad D. Dafik Dafik Dafik Della Putri Anggraeni Dimas Anditha Cahyo Sujiwo Emyus, Ahmad Zaki Endra Priawasana Eric Dwi Putra Fathurrohman, Wafiq Fikria, Nuraeni Mauliddatul Hadiprayogo, Basuki Ika Hesti Agustin, Ika Hesti Imam Gozali Irvan Kholid, Muhammad Ismail Naci Cangul Kafi, Muhamad Kiki Pangestu Kurniawati, Elsa Yuli Muhammad Fadli Muhammad Kutbi Muhammad Kutbi N. Mohanapriya Nur Fadilah, Siti Nuraeni Mauliddatul Fikria panglipur, indah rahayu Restiana Fitri, Syarifah Ridho Alfarisi, Ridho Ridwan Al Fani, Muhammad Rosita, Merlinda Setyaningsih Yuanita Wulandari Silvia, Zulfa Siswono, Hendrik Soleha, Siti Sulisawati, Dwi Noviani Sunyoto, Doni Tanaya Yonas, Cory Ukas Alif Fuadi Widy Priyanti, Putri Zusfindhana, Inna Hamida