A generalized shackle of any graph <i>H</i> admits a super <i>H</i>-antimagic total labeling

Dafik, Dafik; Hasan, Moh.; Azizah, Yuli Nur; Agustin, Ika Hesti

doi:10.1088/1742-6596/893/1/012042

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…Shackle dari graf H dinotasikan dengan G = shack(H, v, n) adalah graf G yang dibangun dari graf non trivial H 1 , H 2 , ..., H n sedemikian hingga untuk setiap 1 ≤ s, t ≤ n, H s dan H t tidak memiliki titik penghubung dimana |s − t| ≥ 2 dan untuk setiap 1 ≤ i ≤ n − 1, H i dan H i+1 memiliki tepat satu titik bersama v, disebut dengan titik penghubung dan k −1 titik penghubung tersebut adalah berbeda. Jika G = shack(H, v, n) titik penghubung digantikan dengan subgraf K ⊂ H disebut dengan generalized shackle, dan dinotasikan dengan G = gshack(H, K ⊂ H, n) [1].…”

Section: Pendahuluanunclassified

Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi

Putri

Dafik

Kusbudiono

2021

CGANT. JOU. OF MATH. AND APP.

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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} $gshack({\bf F}_4,e,n)$.

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Section: Pendahuluanunclassified

Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi

Putri

Dafik

Kusbudiono

2021

CGANT. JOU. OF MATH. AND APP.

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“…If the domain is a vertex set V(G) or an edge set E(G), the labelings are called respectively vertex labelings or edge labelings. If the domain is the set of all vertices and edges then the labeling is called a total labeling [5,6,7]. A general survey of graph labelings is found in [8].…”

Section: Introductionmentioning

confidence: 99%

On the local vertex antimagic total coloring of some families tree

Putri

Dafik

Agustin

et al. 2018

J. Phys.: Conf. Ser.

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“…We recall a partition { , } ( , ) introduced in [4]. We will use the partition for a linear combination in developing a bijection of vertex and edge label of the main theorem.…”

Section: Introductionmentioning

confidence: 99%