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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Jurnal Didaktik Matematika Palapa: Jurnal Study Keislaman dan Ilmu Pendidikan REiD (Research and Evaluation in Education) Jurnal Penelitian Pendidikan IPA (JPPIPA) Pendas : Jurnah Ilmiah Pendidikan Dasar SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan BAHTERA : Jurnal Pendidikan Bahasa dan Sastra Jurnal Pengabdian Masyarakat Sains Indonesia (Indonesian Journal Of Science Community Services) Jurnal Ilmiah Profesi Pendidikan Mandalika Mathematics and Educations Journal Journal of Classroom Action Research Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Teknologi Informatika dan Komputer Griya Journal of Mathematics Education and Application Rengganis Jurnal Pengabdian Masyarakat Unram Journal of Community Service (UJCS) Jurnal Pijar MIPA Jurnal Pendidikan dan Pengabdian Masyarakat Action Research Journal Sigma&Mu: Journal of Mathematics, Statistics and Data Science
Amrullah Amrullah
Departement Of Mathematics, University Of Mataram, Jl. Majapahit No. 62 Mataram, Indonesia
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Journal : Electronic Journal of Graph Theory and Applications (EJGTA)

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The partition dimension of a subdivision of a homogeneous firecracker Amrullah Amrullah
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.2.20

Abstract

Finding the partition dimension of a graph is one of the interesting (and uncompletely solved) problems of graph theory. For instance, the values of the partition dimensions for most kind of trees are still unknown.  Although for several classes of trees such as paths, stars, caterpillars, homogeneous firecrackers and others, we do know their partition dimensions.  In this paper, we determine the partition dimension of a subdivision of a particular tree, namely homogeneous firecrackers. Let G be any graph. For any positive integer k and e \in E(G), a subdivision of a graph G, denoted by S(G(e;k)), is the graph obtained from G by replacing an edge $e$ with a (k+1)-path. We show that the partition dimension of S(G(e;k)) is equal to the partition dimension of G if G is a homogeneous firecracker. We show that the partition dimension of S(G(e;k)) is equal to the partition dimension of G if G is a homogeneous firecracker. 
Co-Authors A. Wahab Jufri Abdul Haris Munandar Ahmad Badawi Aliyatul Himmah Amelia Kusuma Andri Okta Firmansyah Anna Citra Islamiyah Annisa Annisa Arifuddin Arifuddin Arjudin Arjudin Arjudin Arjudin Atiqa Firdaus Awwalus Sanatil Hijriati Baharuddin Baharuddin Baidowi Baidowi Baiq Anita Rahayu Bq. Nerik Prawita Caesarla Elintang Yolawati Darajatul Khunul Khotimah Darojatun Fikri Dedi Riyan Rizaldi Deni Deni Deni Hamdani Dian Endang Lestari Eka Kurniawan Eka Kurniawan Ekky Irza Afriansyah Ery Nurjayanto Farizal Ramadhan Farizal Wahyu Trigantara Faturahman Faturahman Feby Attina Sari Gossani Puja Lestari H. Lalu Nurtaat Hapipi Hapipi Hardika Budianto Harry Soeprianto Harry Soeprianto Herman Firdaus Hidayanti, Gusma Husnul Lail I Nyoman Sridana I. M. Sujana Iftahul Muhayana Jihan Fahira Juliyanti Juliyanti Junaidi Junaidi Junaidi Junaidi Junaidi Ketut Sarjana Ketut Sarjana KETUT SARJANA, KETUT Kurniawan, Eka Laila Hayati Laila Hayati, Laila Laili Gadis Hasanah Lalu Ali Wardana Lalu Nurtaat Lalu Riki Gita Sukma M. Khairul Miswari M. L. Ilhamdi M. Satria Ramanda Mar'atun Atun Mariamah Mariamah Mh Isnaeni Muh. Makhrus Muhammad Arifuddin Muhammad Fadjri Muhammad Turmuzi Muhammda Faisal Khatami Muslim Muslim Nani Kurniati Nani Kurniati Nani Kurniati Ni Made Ayu Ulandari Ni Made Intan Kertiyani Nilwan Nina Muthmainnah Nourma Nourma Nourma Pramestie Wulandari Nur Asniati Nurdianti Nurdianti Nurul Hikmah NURUL HIKMAH Nurul Hikmah Nurul Indah Nurul Pratiwi Nyoman Sridana Nyoman Sridana Nyoman Sridana Prayitno S Putri Husnul Khotimah Rahmani , Irma Reksa Haniantara Reni Sugihartini Richard Yesaya Simanjuntak Ridha Wahidatul Ilmi Riki Tarnanda S. Hadisaputra Salsabila, Nilza Humaira Sangga Patih Alam Santi Farmasari Septiyana Kurnia Hartatin Sinta Baiq Sinta Silviana Muslim Sri Romlawati Sri Seno Handayani Sri Seno Handayani Sri Subarinah Sri Subarinah Sri Subarinah Sri Subarinah Sri Subarinah4 Sridana Sridana Sripatmi Sripatmi Sripatmi Sripatmi Suci Fatmala Sari Sudi Prayitno Sudi Prayitno Sukardi Sukardi Syahrul Azmi Syahrul Azmi Syarifah Umdah Maryam Tabita Wahyu Triutami Tabita Wahyu Triutami Tri Rahayu Agustina Udin Udin Ulfa Lu’luilmaknun Ulfa Lu’luilmaknun Vetty Sugiarty Vivi Rachmatul Hidayati Wahidaturrahmi Wahidaturrahmi, Wahidaturrahmi Widiati Wulandari, Nourma Pramestie Zanirah Permatasari Ziadatul Fatimah