Total Labeling Research Articles

Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext

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.

A case study of an edge-magic total labeling of (a,b)-cycle books

Suppose α and β be the order and size of a graph G respectively. A one-one function h which maps the set of vertices and edges of a graph G onto the integers 1, 2, 3, …, α + β such that h(u) + h(uv) + h(v) = c for any edge (uv) ε E(G) is called an edge-magic total labeling of If h(u) ε {1,2, …, α} for any uεV(G) then h is a super edge-magic total labeling of G. One of interesting research topic is super edge-magic total labeling of cycle book. A cycle book B(a, m, b, n, t) is made up from m copies of cycle Ca and n copies cycle Cb with a commont path Pt . Super edge-magic total labeling of a cycle book B(a, m, b, n, 2) is still under investigation even for the case a = b This paper talk about a partial solution to this problem. We prove that a cycle book B(5, 2, 3, n, 2) has a super edge-magic total labeling for all positive integr n. In addition, we show that a cycle book B(5, 2, 3, n, 2) have an edge-magic total labeling for an integer n, 1 ≥ n ≥ 6.

On local super antimagic total face coloring and the application in developing a cipher block chaining key

There is a specific complexity in the use of IOT, especially in maintaining a secure data transaction. We need a good cryptosystem, since the best encryption key relays on the management cryptosystem. The biggest problem, then, is how to encrypt the plaintext into a ciphertext as hard as possible. We attempt to use the local super antimagic total face coloring of graph in developing a cipher block chaining key. By a local super antimagic total face coloring, we mean a bijection from the set of vertices, edges, and faces to {1, 2, 3, … |V(G)|+|E(G)|+|F(G)|} such that any adjacent two faces f 1 and f 2 will receive a different weights w(f 1) ≠ w(f 2) for f 1, f 2 ∈ F(G). If we use the weights as the color of all faces, the local super antimagic total face labeling is said to be a local super antimagic total face coloring. The minimum number possible to color all faces is called the local antimagic total face chromatic number, denoted by γlatf (G). Once, this resulting coloring in hand, we can develop a cipher block chaining key. We describe the results in the following two algorithms.

Super total graceful labeling of some trees

A graph labeling is an assignment of integers to the edges, vertices, or both of a graph so that it meets to certain conditions. A graph labeling is called total labeling if labeling is given to edges and vertices. Let G be a simple and finite graph having vertex set V(G), edge set E(G), number of vertices p, and number of edges q. A super total graceful labeling of G is a bijection f from V(G) ∪ E(G) to the set {1,2,3,….,p + q} such that f(uv) = |f(u) – f(v)| for every uv ∈ E(G) and f(E(G)) = {1,2,3,…, q}. A graph that admits a super total graceful labeling is called a super total graceful graph. In this paper we show that star graph K 1,n , spider graph SP(1 n , 2 m ), and caterpillar graph P 3⨀nK 1 are super total graceful graphs.

4 – Total Mean Cordial Labeling of Union of Graphs with Star and Bistar

In this paper we investigate 4- total mean cordinality of some union of graphs with star and bistar.

(3,1) – total labeling of cycle, path graphs and some related graphs

The (3,1)- total labeling of a graph G is an assignment of non- negative integers to vertices and edges of G such that no two adjacent vertices or edges have the same label and the difference of labels between a vertex and its incident edges is at least 3. In this paper, we study the (3,1)- total labeling for some types of graphs and derive their (3,1)- total labeling number.

Local super anti-magic total face coloring on shackle graphs

We define graph G as a nontrivial, finite, connected graph which contains vertex set V (G), edge set E(G), and face set F (G). We also define g as bijective function that mapping vertex, edge, and face labeling to natural number which starting from 1 until |V(G)| for vertex label, from |V(G)| + 1 until |V(G)| + |E(G)| for edge label, and the last for face label from |V (G)| + |E(G)| + 1 until |V (G)| + | E (G)| + |F(G)|. If there are different weights in any neighboring two faces f1 and f2 has w(f1) = w(f2) for f1, f2 G F (G), so g is considered a local super anti-magic total face labeling. A proper face coloring from local super anti-magic total face labeling caused by assigns the color of face weights to local super anti-magic total face coloring. The minimum number of colors needed for local super anti-magic total face coloring is called The chromatic number of the local super anti-magic total face coloring. γlatf (G) can be denoted as the chromatic number of the local super anti-magic total face coloring. Encryption keys can possibly be created from the result of local super anti-magic total face coloring that can be used to construct a modified Affine cipher and Cipher Feedback Mode. As a result, we have one the orem for the chromatic number of local super anti-magic total face coloring and two algorithms for establishing super anti-magic total face coloring on shackle graphs in Cipher Feedback Mode.

Local antimagic vertex total coloring on fan graph and graph resulting from comb product operation

Let G = (V,E) be a connected graph with |V|=n and |E|=m. A bijection f: V(G) U E(G) → {1,2,3, …,n + m} is called local antimagic vertex total coloring if for any two adjacent vertices u and v, wt(u)≠ wt(v), where wt(u) = ∑e∈E(u) f(e) + f(u), and E (u) is a set of edges incident to u. Thus any local antimagic vertex total labeling induces a proper vertex coloring of G where the vertex v is assigned the color wt (v). The local antimagic vertex total chromatic number χ1να t(G) is the minimum number of colors taken over all colorings induced by local antimagic vertex total. In this paper we investigate local antimagic vertex total coloring on fan graph (Fn) and graph resulting from comb product operation of Fn and F3 which denoted by Fnt> F3. We get two theorems related to the local antimagic vertex total chromatic number. First, χ1να t(Fn) = 3 where n> 3. Second, 3 < χ1ναt(Fn > F3) < 5 where n > 3.

The vertex coloring of local antimagic total labeling on corona product graphs

Let G be a graph with the vertex set V(G) and edge set E(G). A function h is a bijective function of domain the union of vertex set and edge set of G and range the natural number {1, 2, 3,… , |V(G)| + |E(G)|. We called the function h as a vertex local antimagic total labeling if for any two adjacent vertices x and x‘, w(x) = w(x’), where w(x) = ∑e∈(x) h(e) + h(x), and E(x) is the set of edges which are incident to x. It is considered to be a proper coloring on vertices of graph G if we assign colour to all vertices with w(x). The minimum number of colors by the vertex local antimagic total labeling of G is called the vertex local antimagic chromatic number, denoted by Xlat(G). We study on the vertex local antimagic total labeling of graphs and determined chromatic number on some corona product graphs, namely corona (G © Cm) where G is isomorphis with path, star, broom, cycle, and sunlet graph.

Strong edge antimagic total labeling on multistar

Strong edge antimagic total labelling of a simple graph G(V,E) is graph labelling which the vertex labels are consecutive integers from 1 to |V| such that, the weight of edges, i.e. the total label of the vertices incident to the edge, will form an ascending arithmetic sequence. This article discusses this kind of vertex labelling on multistar graphs. A multistar graph is an unconnected combination of star graphs. The study is a literature study with a mathematical proof. The results of the study is that multistar graphs have a strong edge antimagic total labelling. Furthermore, the labelling can be done on an unconnected combination of m star graphs and the difference of the weight of the edges are 1 and 2 with initial term and , respectively.

Super magic deficiency of graphs

An edge-magic total (EMT) labeling for graph Γ is one-one map from π : V(Γ) ∪ E(Γ) → {1, 2, … ,|V(Γ)|+|E(Γ)|}, so that there manage a number c along a rule that for every edge, uv ∈ E(Γ), π (u) + π (uv) + π (v) = c. And if all vertices are assigned with positive integral numbers {1, 2, … ,|V(Γ)|} then this type of labeling is called a super EMT labeling. Super edge-magic, deficiency for graph Γ, represented as μs (Γ), which is least positive integral number n so that Γ∪ nK 1 has super EMT labeling, or ∞, if there does not exist n. In present article, compute a super edge-magic deficiency for the graph .

An application of super mean and magic graphs labeling on cryptography system

An edge-magic total (EMT) labeling on a simple graph G with p vertices and q edges is a bijection f: V∪E→{1, 2, …, p + q} such that for each edge xy of G, f(x) + f(xy) + f(y) = k, for a fixed positive integer k. Moreover, an EMT labeling f is a super edge-magic total labeling (SEMT) if f(V) = {1, 2, …, p}. Furthermore, a graph G is called a super mean (SM) graph if there exists an injective function f from the vertices of G to {0,1,2,…,q} such that when each edge uv is labeled with (f(u) +f(v))/2 when f(u) +f(v) is even, and (f(u) +f(v) + 1)/2 when f(u) +f(v) is odd, then the resulting edge labels are distinct. There are two essentials results that will be proposed in this paper. In the first result, we show that a graph (n, 1) − F Caterpillar has a SM labeling and a graph Hu,y has a SEMT labeling. In the second result, we will give an application of these labeling to increase the security level of Affine Cipher in which to encrypt a text on socials media.

A general model to optimise CuII labelling efficiency of double-histidine motifs for pulse dipolar EPR applications.

Electron paramagnetic resonance (EPR) distance measurements are making increasingly important contributions to studies of biomolecules underpinning health and disease by providing highly accurate and precise geometric constraints. Combining double-histidine (dH) motifs with CuII spin labels shows promise for further increasing the precision of distance measurements, and for investigating subtle conformational changes. However, non-covalent coordination-based spin labelling is vulnerable to low binding affinity. Dissociation constants of dH motifs for CuII-nitrilotriacetic acid were previously investigated via relaxation induced dipolar modulation enhancement (RIDME), and demonstrated the feasibility of exploiting the dH motif for EPR applications at sub-μM protein concentrations. Herein, the feasibility of using modulation depth quantitation in CuII-CuII RIDME to simultaneously estimate a pair of non-identical independent KD values in such a tetra-histidine model protein is addressed. Furthermore, we develop a general speciation model to optimise CuII labelling efficiency, depending upon pairs of identical or disparate KD values and total CuII label concentration. We find the dissociation constant estimates are in excellent agreement with previously determined values, and empirical modulation depths support the proposed model.

On (p,1)-total labelling of some 1-planar graphs

On (p,1)-total labelling of some 1-planar graphs

(Super)(a, d) - H- Antimagic total labeling of super sub division of cycle

(Super)(a, d) - H- Antimagic total labeling of super sub division of cycle

(3,1) – total labeling of cycle, path graphs and some related graphs

(3,1) – total labeling of cycle, path graphs and some related graphs

Odd Vertex Out-Magic Total Labeling of Some 2-Regular Digraphs

Let D(V, A) be a directed graph of order p and size q. An Odd vertex out-magic total labeling (OVOMTL) of a graph D is bijection f : V(D) ∪ A(D) → {1, 2, … p + q} in order f (V(D)) = {1, 3, …, 2p − 1}, for all υ ∈ V (D), , a constant. A uGo(v) digraph which admits an OVOMTL is termed as Odd Vertex out-magic total (OVOMT). Herein, we emphasize on feature of some 2-regular directed graphs that are Odd Vertex out-magic total (OVOMT).

The total disjoint irregularity strength of some certain graphs

&lt;div class="page" title="Page 1"&gt;&lt;div class="layoutArea"&gt;&lt;div class="column"&gt;&lt;p&gt;&lt;span&gt;Under a totally irregular total &lt;/span&gt;&lt;em&gt;k&lt;/em&gt;&lt;span&gt;-labeling of a graph &lt;/span&gt;&lt;span&gt;&lt;em&gt;G&lt;/em&gt; &lt;/span&gt;&lt;span&gt;= (&lt;/span&gt;&lt;span&gt;&lt;em&gt;V&lt;/em&gt;,&lt;em&gt;E&lt;/em&gt;&lt;/span&gt;&lt;span&gt;), we found that for some certain graphs, the edge-weight set &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;E&lt;/em&gt;&lt;span&gt;) and the vertex-weight set &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;V&lt;/em&gt;&lt;span&gt;) of &lt;/span&gt;&lt;span&gt;&lt;em&gt;G&lt;/em&gt; &lt;/span&gt;&lt;span&gt;which are induced by &lt;/span&gt;&lt;span&gt;&lt;em&gt;k&lt;/em&gt; &lt;/span&gt;&lt;span&gt;= &lt;/span&gt;&lt;span&gt;ts&lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;G&lt;/em&gt;&lt;span&gt;), &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;E&lt;/em&gt;&lt;span&gt;) &lt;/span&gt;&lt;span&gt;∩ &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;V&lt;/em&gt;&lt;span&gt;) is a non empty set. For which &lt;/span&gt;&lt;span&gt;k&lt;/span&gt;&lt;span&gt;, a graph &lt;/span&gt;&lt;span&gt;G &lt;/span&gt;&lt;span&gt;has a totally irregular total labeling if &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;E&lt;/em&gt;&lt;span&gt;) &lt;/span&gt;&lt;span&gt;∩ &lt;/span&gt;&lt;em&gt;W&lt;/em&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;V&lt;/em&gt;&lt;span&gt;) = &lt;/span&gt;&lt;span&gt;∅&lt;/span&gt;&lt;span&gt;? We introduce the total disjoint irregularity strength, denoted by &lt;/span&gt;&lt;span&gt;ds&lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;G&lt;/em&gt;&lt;span&gt;), as the minimum value &lt;/span&gt;&lt;span&gt;&lt;em&gt;k&lt;/em&gt; &lt;/span&gt;&lt;span&gt;where this condition satisfied. We provide the lower bound of &lt;/span&gt;&lt;span&gt;ds&lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;em&gt;G&lt;/em&gt;&lt;span&gt;) and determine the total disjoint irregularity strength of cycles, paths, stars, and complete graphs.&lt;/span&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;/div&gt;

Super Total Labeling (a,d)- edge Antimagic on the Firecracker Graph

An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V (G) ∪ E(G) onto the integers 1, 2, . . . , p + q with the property that the edge-weights, w(uv) = f (u)+ f (v) + f (uv) where uv ∈ E(G),form an arithmetic progression starting from a and having common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge antimagic total labeling of Firecracker Graph.

On the super (a, d)-H-antimagic total labelings of path chain graphs

Super (a, d)-H-antimagic total labeling is closely related to graph labeling, graph decomposition, graph covering and magic square and it arouses more and more people’s concerns. In this paper we study the super (a, d)-H-antimagic total labelings of path chain graph PCG(H,U, n), when d = 0, 1, 2, 3, 4.