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All Journal Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding JTAM (Jurnal Teori dan Aplikasi Matematika) InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS JPMA Emerging Statistics and Data Science Journal

Kusbudiono Kusbudiono, Kusbudiono

Jurusan Matematika FMIPA Universitas Jember

Author-ID : 5286186

Humanities Computer Science & IT Education Environmental Science Mathematics Other

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Articles

Title

Analisa Himpunan Dominasi Lokasi pada Model Topologi Graf Khusus dan Operasinya Reyka Bella Desvandai; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Misalkan $G=(V,E)$ adalah graf sederhana tidak berarah dan terhubung dengan himpunan titik $V$ dan himpunan sisi $E$. Himpunan $D\in V(G)$ dikatakan himpunan dominasi lokasi dari suatu graf terhubung $G$ jika setiap dua titik yang berbeda $u,v \in V(G)\ D$, $N(u)\cap D\neq N(v)\cap D$. Kardinalitas minimal dari himpunan dominasi lokasi disebut nilai himpunan dominasi lokasi dari graf $G$ yang disimbolkan dengan $\gamma_L(G)$. Penelitian ini menghasilkan nilai himpunan dominasi lokasi pada beberapa graf khusus dan operasinya.

Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi Desi Febriani Putri; Dafik Dafik; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Graph coloring began to be developed into coloring dynamic. One of the developments of dynamic coloring is $r$-dynamic total coloring. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph. Total coloring is defined as $c:(V(G) \cup E(G))\rightarrow {1,2,...,k}, k \in N$, with condition two adjacent vertices and the edge that is adjacent to the vertex must have a different color. $r$-dynamic total coloring defined as the mapping of the function $c$ from the set of vertices and edges $(V(G)\cup E(G))$ such that for every vertex $v \in V(G)$ satisfy $|c(N(v))| = min{[r,d(v)+|N(v)|]}$, and for each edge $e=uv \in E(G)$ satisfy $|c(N(e))| = min{[r,d(u)+d(v)]}$. The minimal $k$ of color is called $r$-dynamic total chromatic number denoted by $\chi^{\prime\prime}(G)$. The $1$-dynamic total chromatic number is denoted by $\chi^{\prime\prime}(G)$, chromatic number $2$-dynamic denoted with $\chi^{\prime\prime}_d(G)$ and $r$-dynamic chromatic number denoted by $\chi^{\prime\prime}_r(G)$. The graph that used in this research are path graph, $shackle$ of book graph $(shack(B_2,v,n)$ and \emph{generalized shackle} of graph \emph{friendship} $gshack({\bf F}_4,e,n)$.

Pewarnaan Sisi r-Dinamis pada Graf Khusus dan Graf Operasi Sakel Viqedina Rizky Noviyanti; Kusbudiono Kusbudiono; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let $G=(V(G),E(G))$ be a nontrivial connected graph. The edge coloring is defined as $c:E(G) \rightarrow \{1,2,...,k\}, k \in N$, with the condition that no adjacent edges have the same color. \emph{k}-color \emph{r}-dynamic is an edge coloring of \emph{k}-colors such that each edge in neighboring $E(G)$ is at least min $\{r,d( u)+d(v)-2\}$ has a different color. The dynamic \emph{r}-edge coloring is defined as a mapping of $c$ from $E(G)$ such that $|c(N(uv))|$ = min$\{r,d(u)+d(v)- 2\}$, where $N(uv)$ is the neighbor of $uv$ and $c(N(uv))$ is the color used by the neighboring side of $uv$. The minimum value of $k$ so that the graph $G$ satisfies the \emph{k}-coloring \emph{r}-dynamic edges is called the dynamic \emph{r}-edge chromatic number. 1-dynamic chromatic number is denoted by $\lambda(G)$, 2-dynamic chromatic number is denoted by $\lambda_d(G)$ and for dynamic \emph{r}-chromatic number is denoted by $\lambda_r(G)$. The graphs that used in this study are graph $TL_n$, $TCL_n$ and the switch operation graph $shack(H_{2,2},v,n)$.

Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext Hani'ah Zakin; Ika Hesti Agustin; Kusbudiono Kusbudiono; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let ${H_i}$ be a finite collection of simple, nontrivial and undirected graphs and let each $H_i$ have a fixed vertex $v_j$ called a terminal. The amalgamation $H_i$ as $v_j$ as a terminal is formed by taking all the $H_i$'s and identifying their terminal. When $H_i$ are all isomorphic graphs, for any positif integer $n$, we denote such amalgamation by $G={\rm Amal}(H,v,n)$, where $n$ denotes the number of copies of $H$. The graph $G$ is said to be an $(a, d)$-$H$-antimagic total graph if there exist a bijective function $f: V(G) \cup E(G) \rightarrow \{1, 2,\dots ,|V (G)| + |E(G)|\}$ such that for all subgraphs isomorphic to $H$, the total $H$-weights $w(H)= \sum_{v\in V(H)}f(v)+\sum_{e\in E(H)}f(e)$ form an arithmetic sequence $\{a, a + d, a +2d,...,a+(t - 1)d\}$, where $a$ and $d$ are positive integers and $t$ is the number of all subgraphs 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 study a super $(a, d)$-$H$ antimagic total labeling of $G={\rm Amal}(H,v,n)$ and its disjoint union when $H$ is a complete graph.

Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf Wahyu Nikmatus Sholihah; Dafik Dafik; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let $G=(V, E)$ be a set of ordered set $W=\{W_1,W_2, W_3,...,W_k\}$ from the set of vertices in connected graph $G$. The metric dimension is the minimum cardinality of the resolving set on $G$. The representation of $v$ on $W$ is $k$ set. Vector $r(v|W)=(d(v, W_1), d(v, W_2), ...,$ $d(v, W_k))$ where $d(x, y)$ is the distance between the vertices $x$ and $y$. This study aims to determine the value of the metric dimensions and dimension of {\it non-isolated resolving set} on the wheel graph $(W_n)$. Results of this study shows that for $n \geq 7$, the value of the metric dimension and {\it non-isolated resolving set} wheel graph $(W_n)$ is $dim(W_n)=\lfloor \frac{n-1}{2} \rfloor$ and $nr(W_n)=\lfloor \frac{n+1}{2}\rfloor$. The first step is to determine the cardinality vertices and edges on the wheel graph, then determine $W$, with $W$ is the resolving set $G$ if {\it vertices} $G$ has a different representation. Next determine {\it non-isolated resolving set}, where $W$ on the wheel graph must have different representations of $W$ and all $x$ elements $W$ is connected in $W$.

Analisa Antimagicness Super dari Shackle Graf Parasut dan Aplikasinya pada Polyalphabetic Cipher Riza Nurfadila; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Super (\emph{a,d})-$\mathcal{H}$-antimagic total covering on a graph \emph{G}=(\emph{V,E}) is the total labeling of $\lambda$ of \emph {V(G)} $\cup$ \emph{E(G)} with positive integers \{1, 2, 3,\dots ,$|V(G) \cup E(G)|$\}, for any subgraph \emph{H'} of \emph{G} that is isomorphic to \emph{H} where $\sum$ \emph{H'} = $\sum_{v \in V(H)} \lambda (v ) + \sum_{e \in E(H)} \lambda (e)$ is an arithmetic sequence \{\emph{a, a+d, a+2d,\dots,a+(s-1)d}\} where \emph{a}, \emph{d} are positive numbers where \emph{a} is the first term, \emph{d} is the difference, and \emph{s} is the number of covers. If $\lambda(v)_{v \in V} = {1,2,3,\dots,|V(G)|}$ then the graph \emph{G} have the label of super $\mathcal{H}$-antimagic covering. One of the techniques that can be applied to get the super antimagic total covering on the graph is the partition technique. Graph applications that can be developed for super antimagic total covering are \emph{ciphertext} and \emph{streamcipher}. \emph{Ciphertext} is an encrypted message and is related to cryptography. \emph{Stream cipher} is an extension of \emph{Ciphertext}. This article study the super (a,d)-$\mathcal{H}$-antimagic total covering on the shackle of parachute graph and its application in \emph{ciphertext}. The graphs that used in this article are some parachute graphs denoted by \emph{shack}($\mathcal{P}_{m},e,n$).

Analisis rainbow vertex connection pada beberapa graf khusus dan operasinya Ida Ariska; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i1.78

The vertex colored graph G is said rainbow vertex cennected, if for every two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex connected. On this research, will be raised the issue of how to produce graphs the results of some special graph and how to find the rainbow vertex connection. Operation that use cartesian product, crown product, and shackle. Theorem in this research rainbow vertex connection number in graph the results of operations Wd3,m □ Pn,,Wd3,m ⵙ Pn, and shack(Btm,v,n).

Co-Authors Agustina M. Arika Indah Kristiana Aulia, Safira Nur Bagus Arief Setiawan D. Dafik Desi Febriani Putri Desi Febriani Putri Fahreza, Faizal Rifky Hadi Siswanto Hani'ah Zakin I Made Tirta Ida Ariska Ika Hesti Agustin, Ika Hesti Ikhsanul Halikin, Ikhsanul Juliyanto, Bagus Kiswara Agung Santoso Kosala Dwidja Purnomo Kristiana Wijaya Maya Ayu P, Maya Ayu Moh. Hasan Mustafa , Meiunike Indah NURIL AFANDI, NURIL Reggy Valentinnes Septa Jeniusa Reyka Bella Desvandai Riza Nurfadila Rusli Hidayat S Slamin S. M. Yunika Setiawan, Bagus Arief Titis Miranti, Titis Viqedina Rizky Noviyanti Wahyu Nikmatus Sholihah Wanda Olyvia Anggraini, Wanda Olyvia

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