Claim Missing Document
Check
Articles

Found 6 Documents
Search
Journal : CAUCHY

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.
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 ( ).
On Irregular Colorings of Unicyclic Graph Family Arika Indah Kristiana; Dafik Dafik; Qurrotul A’yun; Robiatul Adawiyah; Ridho Alfarisi
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.v7i4.16917

Abstract

Irregular coloring is a proper coloring and each vertex on a graph must have a different code. The color code of a vertex v is  where  and    is the number of vertices that are adjacent to v and colored i. The minimum k-color used in irregular coloring is called the irregular chromatic number and denoted by . In this paper, we discuss the irregular chromatic number for the bull graph, pan graph, sun graph, peach graph, and caveman graph. 
Co-Authors A Arynda A H Rahmatillah A. Y. Harsya Adelia Putri Liowardani Adelia Putri Liowardani Agnes Ika Nurvitaningrum, Agnes Ika Agrita Kanty Purnapraja, Agrita Kanty Agustina M. Agustina Muharromah, Agustina Ahmad Adi Ahmad Musyaffa' Hikamuddin Ahmad Syaiful Rizal, Ahmad Syaiful Aldyon Restu Azkarahman Alfian Yulia Harsya, Alfian Yulia Alfin Nabila Taufik Amalina, Putri Nur Anindyta Anggirena Wulandari Anindyta Anggirena Wulandari Anisa Meilinda Wardani Antonius C. Prihandoko arief fatahillah Arika I. Kristiana Arika Indah Kriatiana Arika Indah Kristiana Arnasyitha Yulianti S, Arnasyitha Arnasyitha Yulianti Soelistya Artanty Nastiti, Artanty Bayu Aprilianto Darian Aji Bawono Desak Made Dwika Saniriati Desi Febriani Putri Desi Febriani Putri Desy Tri Puspasari Desy Tri Puspasari, Desy Tri Devi Eka Wardani M, Devi Eka Dewi ANGGRAENI Dewi Anggraeni Dian Anita Hadi Dian Anita Hadi, Dian Anita Didik Sugeng Didin Trisnani, Didin Dina Tri Djoni Budi Sumarno Dwi Agustin Retnowardani Dyna Probo Mukti Elitta P Dewy Elok Asmaul Husna Elok Asmaul Husna Elsa Yuli Kurniawati Elsa Yuli Kurniawati Elsy Wijayanti Elsy Wijayanti Endang Wahyuningrum Ermita R Albirri Ermita Rizki Albirri Ervin Eka Riastutik Ervin Eka Riastutik, Ervin Eka Ervin Oktavianingtyas Erwinda Viantasari Excelsa Suli Wildhatul Jannah Farah Rezita Nurtaatti, Farah Rezita Fathulloh Faruq Fia Cholidah, Fia Firman Firman Fitri Wulandari Fitri Wulandari Gembong A. W. Hani'ah Zakin Harianto Setiawan, Harianto Hendry Dwi Saputro Herninda Lucky Oktaviana Hilmiyah Hanani Hilmiyah Hanani Hobri I H Agustin I H. Agustin I Ikhwandi I M Tirta I Made Tirta Ida Ariska Ika Hesti A. Ika Hesti Agustin, Ika Hesti Ika Mareta Ika Nur Maylisa Imanul Umar Hawari Imro’atun Rofikah Indar Setiani Indi Izzah Makhfduloh Inge Yosanda Arianti, Inge Yosanda Irma Azizah Irma Azizah, Irma Istamala Idha Retnoningsih Jackson P Mairing Jamhari Jamhari Jesi Irwanto, Jesi Joni Susanto Joni Susanto, Joni Juanda Brahmanto K Kasturi K Khasan, K Karinda Rizqy Aprilia, Karinda Rizqy Khilyah Munawaroh Kholifatu Rosyidah Kholifatur Rosyidah Kiki Kurdianto Kiswara Agung Santoso Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Laily Anisa Nurhidayati Laily Anisa Nurhidayati Lubis Muzaki Lusia Dewi Minarti Lusia Dewi Minarti M. Wildan Athoillah Marsidi Marsidi Miftahur Roifah Millatuz Zahroh, Millatuz Moch. Avel Romanza P Moch. Avel Romanza P, Moch. Avel Romanza Mohammad Fadli Rahman Mohammad Fadli Rahman Muhamad Faizal Fatoni Muhammad Lutfi Asy’ari Muhlisatul Mahmudah Muhlisatul Mahmudah, Muhlisatul N Maylisa N Y. Sari Nabilah Ayu Az-Zahra Nafisa Afwa Sania Nindya Laksmita Dewi, Nindya Laksmita Novalita Anjelia Novalita Anjelia Novian Nur Fatihah Novita Cahya Mahendra Novita Sana Susanti Novri Anggraeni, Novri Nur Alfiyantiningsih Nur Asia Jamil, Nur Asia Nurcholif Diah Sri Lestari Nuris Hisan Nazula Nuryatul Laili Nuwaila Izzatul Muttaqi O A Safiati O. A. Safiati Ojat Darojat Okti Anis Safiati Prihandini, Rafiantika Megahnia Putri Ayu Permatasari Putri Indah Pratiwi Putri Rizky H.P, Putri Rizky Putu Liana Wardani Q Qoriatul QurrotaA’yuniArRuhimat A’yuni ArRuhimat QurrotaA’yuniArRuhimat A’yuni ArRuhimat Qurrotul A’yun Quthrotul Aini Fuidah R Adawiyah R M Prihandini R Ratih R Rohmatullah R. Humaizah Rafiantika M Rafiantika Megahnia Prihandini Randhi N. Darmawan, Randhi N. Randi Pratama Murtikusuma Ratna Syafitri Ratna Syafitri Reza Mega Ardhilia Ridho Alfarisi Ridho Alfarisi, Ridho Riniatul Nur Wahidah Rizki Aulia Akbar Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Rukmana Sholehah Rukmana Sholehah, Rukmana S Slamin S Suciati S Suharto S Sunardi S Susanto S Susanto S Susanto S Susanto S. Chususiyah S. M. Yunika Saddam Hussen Safira Izza Ghafrina Safira Izza Ghafrina Saifudin, Ilham Saniriati, Desak Made Dwika Shapbian Novindasari Shapbian Novindasari, Shapbian Shela Okta Grefina, Shela Okta Sherly Citra Wuni, Sherly Citra Sih Muhni Yunika, Sih Muhni Siska Aprilia Hardiyanti Siska Binastuti Siska Binastuti, Siska Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Siti Mar’atus Sholihah Siti Mar’atus Sholihah Soleh Chudin Sri Tresnaningsih Sufirman Sufirman Suntusia Suntusia Suparti Supratiningsih Supratiningsih Susanto Susanto Susanto Susanto Susi Setiawani Tanti Windartini, Tanti Tasrip Rudiono Tito Putra Mahendratama Sasongko Tommi Sanjaya Putra Toto Bara Setiawan Tri Dyah Prastiti Ulul Azmi Umi Azizah Anwar Viqedina Rizky Noviyanti Vutikatul Nur Rohmah Wahyu Nikmatus Sholihah Wahyu Sulistio Weny Wijayanti Weny Wijayanti, Weny Wicha Dwi Wicha Dwi Vikade, Wicha Dwi Y Yunita Yessy Eki Fajar Reksi Yuli Nur Azizah, Yuli Nur Z R Ridlo Zainur Rasyid Ridlo