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Journal : Indonesian Journal of Combinatorics

On r-dynamic coloring of some graph operations Ika Hesti Agustin; D. Dafik; A. Y. Harsya
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (190.124 KB) | DOI: 10.19184/ijc.2016.1.1.3

Abstract

Let $G$ be a simple, connected and undirected graph. Let $r,k$ be natural number. By a proper $k$-coloring  of a graph $G$, we mean a map $ c : V (G) \rightarrow S$, where $|S| = k$, such that any two adjacent vertices receive different colors. An $r$-dynamic $k$-coloring is a proper $k$-coloring $c$ of $G$ such that $|c(N (v))| \geq min\{r, d(v)\}$ for each vertex $v$ in $V(G)$, where $N (v)$ is the neighborhood of $v$ and $c(S) = \{c(v) : v \in S\}$ for a vertex subset $S$ . The $r$-dynamic chromatic number, written as $\chi_r(G)$, is the minimum $k$ such that $G$ has an $r$-dynamic $k$-coloring. Note that the $1$-dynamic chromatic number of graph is equal to its chromatic number, denoted by $\chi(G)$, and the $2$-dynamic chromatic number of graph has been studied under the name a dynamic chromatic number, denoted by $\chi_d(G)$. By simple observation it is easy to see that $\chi_r(G)\le \chi_{r+1}(G)$, however $\chi_{r+1}(G)-\chi_r(G)$ can be arbitrarily large, for example $\chi(Petersen)=2, \chi_d(Petersen)=3$, but $\chi_3(Petersen)=10$. Thus, finding an exact values of $\chi_r(G)$ is significantly useful. In this paper, we will show some exact values of $\chi_r(G)$ when $G$ is an operation of special graphs.
Local antimagic vertex coloring of unicyclic graphs Nuris Hisan Nazula; S Slamin; D Dafik
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (206.369 KB) | DOI: 10.19184/ijc.2018.2.1.4

Abstract

The local antimagic labeling on a graph G with ∣V∣ vertices and ∣E∣ edges is defined to be an assignment f : E → {1, 2, ⋯, ∣E∣} so that the weights of any two adjacent vertices u and v are distinct, that is, w(u) ≠ w(v) where w(u) = Σe ∈ E(u)f(e) and E(u) is the set of edges incident to u. Therefore, any local antimagic labeling induces a proper vertex coloring of G where the vertex u is assigned the color w(u). The local antimagic chromatic number, denoted by χla(G), is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we present the local antimagic chromatic number of unicyclic graphs that is the graphs containing exactly one cycle such as kite and cycle with two neighbour pendants.
Implementation of super H-antimagic total graph on establishing stream cipher Antonius Cahya Prihandoko; D. Dafik; Ika Hesti Agustin
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (308.19 KB) | DOI: 10.19184/ijc.2019.3.1.2

Abstract

This paper is aimed to study the use of super (a, d)-H antimagic total graph on generating encryption keys that can be used to establish a stream cipher. Methodology to achieve this goal was undertaken in three steps. First of all the existence of super (a, d)-H-antimagic total labeling was proven. At the second step, the algorithm for utilizing the labeling to construct a key stream was developed, and finally, the mechanism for applying the key to establish a stream cipher was constructed. As the result, according to the security analysis, it can be shown that the developed cryptographic system achieve a good security.
Co-Authors A Arynda A H Rahmatillah A. Y. Harsya Adawiyah, R 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 Futuhul Hadi Alfian Yulia Harsya, Alfian Yulia Alfin Nabila Taufik Alfiyantiningsih, Nur Amalina, Putri Nur Anindyta Anggirena Wulandari Anisa Meilinda Wardani Annadhifi, Muhammad Ilham Nurfaizi Antonius Cahya Prihandoko Arif Fatahillah Arika I. Kristiana Arika Indah Kriatiana Arika Indah Kristiana Arnasyitha Yulianti S, Arnasyitha Arnasyitha Yulianti Soelistya ArRuhimat, QurrotaA’yuniArRuhimat A’yuni Artanty Nastiti, Artanty Asari, Okta Endri Asy’ari, Muhammad Lutfi Awalin, Qonita Ilmi Aziza, Adinda Putri A’yun, Qurrotul Bawono, Darian Aji Bayu Aprilianto Brahmanto, Juanda Cangul, Ismail Naci 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 Dewy, Elitta P Dian Anita Hadi, Dian Anita Didik Sugeng Didin Trisnani, Didin Dina Tri Djoni Budi Sumarno Dliou, Kamal Dwi Agustin Retnowardani Dyna Probo Mukti Elok Asmaul Husna Elsa Yuli Kurniawati Elsa Yuli Kurniawati Endang Wahyuningrum Ermita R Albirri Ermita Rizki Albirri Ervin Eka Riastutik, Ervin Eka Ervin Oktavianingtyas Excelsa Suli Wildhatul Jannah Farah Rezita Nurtaatti, Farah Rezita Faruq, Fathulloh fatahillah, arief Fatoni, Muhamad Faizal Fia Cholidah, Fia Firdausiyah, Iftitahul Firman Firman Fitri Wulandari Gembong A. W. Hani'ah Zakin Harianto Setiawan, Harianto Hendry Dwi Saputro Herninda Lucky Oktaviana Hilmiyah Hanani Hobri Husain, Sharifah Kartini Said I H Agustin I H. Agustin I Ikhwandi I M Tirta I Made Tirta I Made Tirta Ida Ariska Ika Hesti A. Ika Hesti Agustin, Ika Hesti Ika Mareta 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 Jannah, Excelsa Suli Wildhatul Jesi Irwanto, Jesi Joni Susanto, Joni K Kasturi K Khasan, K Karinda Rizqy Aprilia, Karinda Rizqy Khilyah Munawaroh Kholifatu Rosyidah Kholifatur Rosyidah Khusnul, Agustina Hotimatus Kiki Kurdianto Kiswara Agung Santoso Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Laili, Nuryatul Laily Anisa Nurhidayati Liliek Susilowati Liowardani, Adelia Putri Lubis Muzaki Lusia Dewi Minarti Lusia Dewi Minarti M. Wildan Athoillah Makhfudloh, I I Mardiyah, Fitriyatul Marsidi Marsidi Maylisa, Ika Nur Miftahur Roifah Millatuz Zahroh, Millatuz Moch. Avel Romanza P, Moch. Avel Romanza Mohammad Fadli Rahman Mohanapriya, N. Muhammad Lutfi Asy’ari Muhlisatul Mahmudah, Muhlisatul Mursyidah, Indah Lutfiyatul Murtini Murtini, Murtini N Maylisa N Y. Sari Nabilah Ayu Az-Zahra Nafisa Afwa Sania Nindya Laksmita Dewi, Nindya Laksmita 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 Nuwaila Izzatul Muttaqi O A Safiati O. A. Safiati Ojat Darojat Okti Anis Safiati Permatasari, Putri Ayu Pratiwi, Putri Indah Prihandini, R M Prihandini, Rafiantika Megahnia Prihandini, Rafiantika Megahniah Prihandini, RM Prihandoko, AC Prof. Dr.I Nengah Suparta,M.Si . Pujiyanto, Arif Putra Mahendratama Sasongko, Tito Putri Rizky H.P, Putri Rizky Q Qoriatul QurrotaA’yuniArRuhimat A’yuni ArRuhimat Qurrotul A’yun Quthrotul Aini Fuidah R M Prihandini R Ratih R Rohmatullah R. Humaizah Rafiantika M Rafiantika Megahnia Prihandini Rahmadani, M R Rahman, Md. Saidur Randhi N. Darmawan, Randhi N. Randi Pratama Murtikusuma Ratna Syafitri Reza Mega Ardhilia Ridho Alfarisi Ridho Alfarisi, Ridho Ridlo, Zainur Rasyid Riniatul Nur Wahidah Rizki Aulia Akbar Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Rohini, A Rukmana Sholehah, Rukmana S Slamin S Suciati S Suharto S Sunardi S Susanto S. Chususiyah S. M. Yunika Saddam Hussen Safira Izza Ghafrina Safira Izza Ghafrina Saifudin, Ilham Saniriati, Desak Made Dwika Santoso, Aji Mansur Septory, Brian Juned Shapbian Novindasari, Shapbian Shela Okta Grefina, Shela Okta Sherly Citra Wuni, Sherly Citra Sholihah, Siti Mar’atus Sih Muhni Yunika, Sih Muhni Siska Aprilia Hardiyanti Siska Binastuti Siska Binastuti, Siska Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Siti Mar’atus Sholihah Soleh Chudin Sri Tresnaningsih Sufirman Sufirman Sulistio, Wahyu Sullystiawati, Lusia Herni Sunder, R. Suntusia Suntusia Suparti Supratiningsih Supratiningsih Susanto Susanto Susanto Susanto Susi Setiawani Tanti Windartini, Tanti Tasrip Rudiono Thoyibah, Fifi Tommi Sanjaya Putra Toto Bara Setiawan Tri Dyah Prastiti Ulul Azmi Umi Azizah Anwar Venkatachalam, M. Viantasari, Erwinda Viqedina Rizky Noviyanti Vutikatul Nur Rohmah Wahidah, Riniatul Nur Wahyu Lestari Wahyu Nikmatus Sholihah Wardani, Putu Liana Weny Wijayanti, Weny Wicha Dwi Wicha Dwi Vikade, Wicha Dwi WIHARDJO, EDY Wijayanti, Elsy Y Yunita Yanuarsih, Elly Yessy Eki Fajar Reksi Yuli Kurniawati, Elsa Yuli Nur Azizah, Yuli Nur Z R Ridlo Zainur Rasyid Ridlo