arXiv subjects

Dafik

Publications and source records attributed to Dafik.

3 recordsLinked to original sources

arXiv2024

Enhancing Data Security through Rainbow Antimagic Graph Coloring for Secret-Share Distribution and Reconstruction

Now-a-days, ensuring data security has become an increasingly formidable challenge in safeguarding individuals' sensitive information. Secret-sharing scheme has evolved as a most successful cryptographic technique that allows a secret to be divided or distributed among a group of participants in such a way that only a subset of those participants can reconstruct the original secret. This provides a safe level of security and redundancy, ensuring that no single individual possesses the complete secret. The implementation of Rainbow Antimagic coloring within these schemes not only safeguards the data but also ensures an advanced level of information security among multi-participant groups. Additionally, the retrieved data is reconstructed and can be disseminated to all group participants via multiple rounds of communication.

cs.CR↗

arXiv2022

The Research Based Learning -- STEM Learning Activities: The Use of r-Dynamic Coloring to Improve the Students Metaliteracy in Solving a Tessellation Decoration Problem

The metaliteracy ability is a very important in today's life, especially to live in the disruptive technology era. Metaliteracy is an ability that goes beyond metacognition and technological literacy. However, the students' metalliteracy ability is still relatively low. One of the causes of the low ability is due to the learning model that has been applied so far has not been able to bring out this ability. Therefore, in this study, an RBL learning model that is integrated with the STEM approach will be applied in solving the r-Dynamic coloring problem. By r-dynamic coloring, we mean a proper k-coloring c of G if for every vertex v in V (G) satisfies the number of neighbours color is greater then min{r,d(v)}. The minimum k such that G has an r-dynamic coloring with k colors is called an r-dynamic chromatic number, denoted by r(G). By using the r-dynamic coloring technique, we will improve students' metaliteracy in solving the tessellation decoration problem. Therefore, in this research, the syntax of learning activities of the Research-Based Learning and STEM approach will be developed including the assesment indicator of the metaliteracy ability.

physics.ed-ph↗

arXiv2021

A study of a combination of distance domination and resolvability in graphs

For $k \geq 1$, in a graph $G=(V,E)$, a set of vertices $D$ is a distance $k$-dominating set of $G$, if any vertex in $V\setminus D$ is at distance at most $k$ from some vertex in $D$. The minimum cardinality of a distance $k$-dominating set of $G$ is the distance $k$-domination number, denoted by $\gamma_k(G)$. An ordered set of vertices $W=\{w_1,w_2,\ldots,w_r\}$ is a resolving set of $G$, if for any two distinct vertices $x$ and $y$ in $V\setminus W$, there exists $1\leq i\leq r$, such that $d_G(x,w_i)\neq d_G(y,w_i)$. The minimum cardinality of a resolving set of $G$ is the metric dimension of the graph $G$, denoted by $dim(G)$. In this paper, we introduce the distance $k$-resolving dominating set, which is a subset of $V$ that is both a distance $k$-dominating set and a resolving set of $G$. The minimum cardinality of a distance $k$-resolving dominating set of $G$ is called the distance $k$-resolving domination number and is denoted by $\gamma^r_k(G)$. We give several bounds for $\gamma^r_k(G)$ some in terms of the metric dimension $dim(G)$ and the distance $k$-domination number $\gamma_k(G)$. We determine $\gamma^r_k(G)$ when $G$ is a path or a cycle. Afterwards, we characterize the connected graphs of order $n$ having $\gamma^r_k(G)$ equal to $1$, $n-2$, and $n-1$, for $k\geq 2$. Then, we construct graphs realizing all the possible triples $(dim(G),\gamma_k(G),\gamma^r_k (G))$, for all $k\geq 2$. Later, we determine the maximum order of a graph $G$ having distance $k$-resolving domination number $\gamma^r_k(G)=\gamma^r_k\geq 1$, we provide graphs achieving this maximum order for any positive integers $k$ and $\gamma^r_k$. Finally, we establish Nordhaus-Gaddum bounds for $\gamma^r_k(G)$, for $k\geq 2$.

math.CO↗