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Arika Indah Kristiana
Universitas Jember
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Journal : UNEJ e-Proceeding

 1 
On Total r-Dynamic Coloring of Several Classes of Graphs and Their Related Operations Kusbudiono Kusbudiono; Desi Febriani Putri; Dafik Dafik; Arika Indah Kristiana
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

All graphs in this paper are simple, connected and undirected. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. A total r-dynamic coloring is a proper k-coloring c of G, such that ∀v ∈ V (G), |c(N(v))| ≥ min[r, d(v) + |N(v)|] and ∀uv ∈ E(G), |c(N(uv))| ≥ min[r, d(u) + d(v)]. The total r-dynamic chromatic number, written as χ ′′r (G), is the minimum k such that G has an r-dynamic k-coloring. Finding the total r-dynamic chromatic number is considered to be a NP-Hard problems for any graph. Thus, in this paper, we initiate to study χ′′ r (G) of several classes of graphs and and their related operations.
Co-Authors Afni, Anis Nur Agatha, Alvian Bagus Ahmad Aji Aima, Muslihatul Aji, Ahmad Arif Fatahillah Arifandi, Agus Asy’ari, Muhammad Lutfi Aziza, Adinda Putri Azizah, Zakiyah Lina Nur A’yun, Qurrotul Bunga Ayu Desy Permatasari, Bunga Ayu Cahyadewi, Karina Cindy Cici Fitri Lestari, Cici Fitri D Dimas, D D. Dafik Dafik Deddy Setiawan Deddy Setiawan Deddy Setyawan Desi Febriani Putri Devira Ayu Nurandari, Devira Ayu Dewi Santi, Dewi Dewi, Ernita Sukarno Dian Kurniati Didik Sugeng Pambudi Dimas Ardiansyah Ramadhan Dinar Dwi Yuliyanti Dinawati Trapsilasiwi Dliou, Kamal Dwi Agustin Retnowardani Dwi Roby Pramono Dwi Sylvia Hanafi Edy Wihardjo Eka Cahya Lestari, Eka Cahya Eka Wulandari Fauziah, Eka Wulandari Eko Gunariyanto Elsa Yuli Kurniawati Ema Desia Prajitiasari Erica Dian P Ermita Rizki Albirri Ernita Sukarno Dewi, Ernita Fatimah, Laila Nurul Fihrisi, Fathan Hobri I Made Tirta I Made Tirta Intan Nurul Awwaliyah Islamiah, Maulidi Arsih Umaroh Ja'far, Muhammad Jatmiko, Dhanar Dwi Hary Karina Cindy Cahyadewi Karuniaji Fitra Insani Khilyah Munawaroh Khusnul, Agustina Hotimatus Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Kusumawati, Nurita Lestari, Deninta Dwi Ayu Lestari, Nurcholif Diah Sri Lioni Anka Monalisa, Lioni Anka Marmono Singgih Miftahul Jannah Mohammad Fadli Rahman Muhammad Gufronil Halim Muhammad Lutfi Asy’ari Muhammad Usaid Hudloir Murtini Murtini, Murtini Niswatul Imsiyah Nur Safrida, Lela Nurbuono, Mousthapaa Nurcholif Diah Sri Lestari Nurina Anggun Ratnaningtyas Nuroeni, Ilmiatun Osman, Sharifah Prahastiwi, Lusi Rizzami Pratiwi, Alfiani Dyah Prihandini, Rafiantika M. Prihandini, Rafiantika Megahniah Pujiyanto, Arif Putra, Aldi Maulana Qurrotul A’yun Rafelita Faradila Sandi Rafiantika Megahnia Prihandini Rahmawati, Mira Randi Pratama Murtikusuma Ratna Dwi Christyanti, Ratna Dwi Retno Nur Khasanah Ridho Alfarisi Ridho Alfarisi, Ridho Ridlo, Zainur Rasyid Rizky Astarina, Rizky Robiatul Adawiyah Robiatul Adawiyah S Suharto S Sunardi S Susanto Saddam Hussen Santoso, Aji Mansur Saputra, Guntari Setiawan, Renal Heldi Siddiqui, M. Kamran Siti Aisyah Slamin Sumani . Surya Indriani Susanto Susanto Susanto, Arnis Budi Susi Setiawani Syahputri, Vika Thoyibah, Fifi Tika Nurpitasari Titik Sugiarti Titin Kartini Toto Bara Setiawan Umi Azizah Anwar WIHARDJO, EDY Wirdah Pramita N Yanuarsih, Elly Zainur Rasyid Ridlo