Fakultas Matematika dan Ilmu Pengetahuan Alam
https://repository.unej.ac.id/xmlui/handle/123456789/10828
2024-03-28T21:13:45ZSuper (a,d)-{H}-Antimagic Total Selimut pada Amalgamasi Graf Roda untuk Pengembangan Kriptosistem Polyalphabetic
https://repository.unej.ac.id/xmlui/handle/123456789/73332
Super (a,d)-{H}-Antimagic Total Selimut pada Amalgamasi Graf Roda untuk Pengembangan Kriptosistem Polyalphabetic
Novri Anggraeni., Dafik., Slamin
A graph $G(V,E)$ has a $\mathcal{H}$-covering if every
edge in $E$ belongs to a subgraph of $G$ isomorphic to
$\mathcal{H}$. An $(a,d)$-$\mathcal{H}$-antimagic total covering is
a total labeling $\lambda$ from $V(G)\cup E(G)$ onto the integers
$\{1,2,3,...,|V(G)\cup E(G)|\}$ with the property that, for every
subgraph $A$ of $G$ isomorphic to $\mathcal{H}$ the
$\sum{A}=\sum_{v\in{V(A)}}\lambda{(v)}+\sum_{e\in{E(A)}}\lambda{(e)}$
forms an arithmetic sequence. A graph that admits such a labeling is
called an $(a,d)$-$\mathcal{H}$-antimagic total covering. In
addition, if $\{\lambda{(v)}\}_{v\in{V}}=\{1,...,|V|\}$, then the
graph is called $\mathcal{H}$-super antimagic graph. In this paper
we study $\mathcal{H}$-covering of amalgamation of wheel graph and
also to develop polyalphabetic chiper of cryptosystem from a secret
massage.
2016-02-18T00:00:00ZPelabelan Super ({\it a,d})-${\mathcal {H}}$-Antimagic Total Dekomposisi pada Graf Windmill
https://repository.unej.ac.id/xmlui/handle/123456789/73331
Pelabelan Super ({\it a,d})-${\mathcal {H}}$-Antimagic Total Dekomposisi pada Graf Windmill
Misi Devi Milasari., Ika Hesti A., Dafik
Diberikan suatu graf G sedehana, dan tidak
berarah. $f(V)=\{1,2,3,...,p\}$ dan $f(E)=\{p+1,...,p+q\}$ dikatakan
sebagai pelabelan super. Pelabelan super ({\it a,d})-${\mathcal
{H}}$-antimagic total selimut merupakan suatu graf $G=(V(G),E(G))$
dengan $H$ merupakan subgraf dari $G$ dimana untuk setiap sisinya
termuat dalam subgraf $H$ dan $G$ isomorfik dengan $H$. Suatu graf
$G=(V,E)$ dikatakan memuat selimut $\mathcal{H}$=$\{H_1, H_2,
\ldots, H_k\}$ dengan sifat setiap sisi di $G$ termuat
sekurang-kurangnya satu graf $H_i$ yang isomorfik dengan subgraf $H$
untuk suatu $i \epsilon \{1, 2, 3,\ldots, k\}$. Pelabelan selimut
$\mathcal{H}$-antimagic pada graf $G$ adalah sebuah fungsi bijektif
sehingga terdapat jumlahan yang merupakan barisan aritmatika
$\{a,a+d,a+2d,\ldots,a+(t-1)d\}$. Jika selimut-$\mathcal{H}$
mempunyai sifat setiap sisi dari graf $G$ termuat tepat satu pada
graf $H_{i}$ untuk $i \in\{1,2,...,k\}$ maka selimut-$\mathcal{H}$
disebut dekomposisi-$\mathcal{H}$. Pada artikel ini, akan dikaji
mengenai keberadaan super $(a,d)$-$WD_5$ antimagic total dekomposisi
pada graf $Windmill$, yang dinotasikan dengan $WD_5^n$.
2016-02-18T00:00:00ZPelabelan Super (a,d)- {H} Antimagic Total Dekomposisi pada Shakel dari Graf Kipas Konektif
https://repository.unej.ac.id/xmlui/handle/123456789/73330
Pelabelan Super (a,d)- {H} Antimagic Total Dekomposisi pada Shakel dari Graf Kipas Konektif
Fia Cholidah., I. H. Agustin., Dafik
All graph in this paper are finite, simple
and undirected. By $H'$-covering, we mean every edge in $E(G)$
belongs to at least one subgraph of $G$ isomorphic to a given graph
$H$. A graph $G$ is said to be an $(a, d)$-${\mathcal
{H}}$-antimagic total decomposition 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 $H'$ isomorphic to ${\mathcal
{H}}$, the total ${\mathcal {H}}$-weights $w(H)= \sum_{v\in
V(H')}f(v)+\sum_{e\in E(H')}f(v)$ form an arithmetic sequence $\{a,
a + d, a +2d,...,a+(s - 1)d\}$, where $a$ and $d$ are positive
integers and $s$ is the number of all subgraphs $H'$ isomorphic to
${\mathcal {H}}$. Such a labeling is called super if $f: V(G)
\rightarrow \{1, 2,\dots ,|V (G)|\}$. In this paper, we study the
problem that if a connected graph $G$ is super labelling $(a,
d)-{\mathcal {H}}$- antimagic total decomposition, is the connective
of the graph $G$ super $(a, d)$-${\mathcal {H}}$ - antimagic total
decomposition as well? We will answer this question for the case
when the graph $G$ is a shackle of $SF_4^3$ and ${\mathcal {H}}$=$F_4$ isomorphic to $H$.}
2016-02-18T00:00:00ZSuper $(a,d)$ - Face Antimagic Total Labeling of Shackle of Cycle Graph
https://repository.unej.ac.id/xmlui/handle/123456789/73329
Super $(a,d)$ - Face Antimagic Total Labeling of Shackle of Cycle Graph
F.R Nurtaatti., Dafik., A.I Kristiana
A graph $G$ of order $p$, size $q$ and face $r$ is called a super
$(a,d)$ - face antimagic total labelling, if there exist a bijection
$f:V(G)\bigcup E(G)\bigcup F(G)$ $\rightarrow \{1,2,...,p+q+r\}$
such that the set of $s$-sided face
weights,$W_{s}=\{a_{s},a_{s}+d,a_{s}+2d,...,a_{s}+(r_{s}-1)d\}$ form
an arithmetic sequence for some integers as and common difference
$d$ and $r_{s}$ is the number of $s$-sided faces. Such a graph is
called super if the smallest possible labels appear on the vertices.
In this paper we will study the existence on super $(a,d)$ - face
antimagic total labeling of Shackle $C_6^1$ and it can be used to
develop a secure poly alphabetic cryptosystem
2016-02-18T00:00:00Z