Edge-antimagic Total Labeling Research Articles

ON SUPER (3n+5,2)- EDGE ANTIMAGIC TOTAL LABELING AND IT’S APPLICATION TO CONSTRUCT HILL CHIPER ALGORITHM

Graph labeling can be implemented in solving problems for various fields of life. One of the application of graph labelling is in security system. Information security is needed to reduce risk, data manipulation, and unauthorized destruction or destruction of information. Cryptographic algorithms that can be used to build security systems, one of the cryptographic algorithms is Hill Cipher. Hill chipper is a cryptographic algorithm that uses a matrix as a key to perform encryption, decryption, and modulo arithmetic. This study discusses the use of Super (3n+5,2)- edge antimagic total labeling to construct the Hill Chiper algorithm. The variation of the edge weight function and the corresponding edge label on the graph, will make the constructed lock more complicated to hack

Computing Antimagic Labeling of Lattically Designed Symmetric Networks

In this article, we address the super edge-antimagic total labeling of the hexagonal lattice HTTm,n and two non-isomorphic forms of prismatic lattice PTTm,n. The aforementioned classes are symmetric lattices involving the finite chain of tripartite networks. Our article further closes with the summary, 3D- graphical illustrations and a practical example of our findings.

On Super (a,d)-edge antimagic total labeling of branched-prism graph

Let <em>H</em> be a branched-prism graph, denoted by <em>H</em> = (<em>C<sub>m</sub></em> x <em>P</em><sub>2</sub>) ⊙ Ǩ<sub>n</sub> for odd <em>m</em>, <em>m</em> ≥ 3 and <em>n</em> ≥ 1. This paper considers about the existence of the super (<em>a</em>,<em>d</em>)-edge antimagic total labeling of <em>H</em>, for some positive integer <em>a</em> and some non-negative integer <em>d</em>.

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.

Super (a; d)-edge Antimagic Total Labeling of Shack(F6; B2; n) Graph for Developing a Polyalphabetic Cryptosystem

A graph G of order p and size q is called an (a; d)-edge-antimagic total if there exist a bijection f : V (G) [ E(G) ! f1; 2; : : : ; p + qg such that the edge-weights, w(uv) = f(u) + f(v) + f(uv); uv 2 E(G), form an arithmetic sequence with ¯rst term a and common di®erence d. Such a graph is called super if the smallest possible labels appear on the vertices. In this paper we study a super edge-antimagic total labeling of Shackle (F6; B2; n) Graph connected and we will use it to develop a polyalphabetic cryptosystem.

Super edge local antimagic total labeling of some graph operation

Let G be a simple connected, and undirected graph. Graph G has a set of vertex denoted by V(G) and a set of edge denoted by E(G). d(v) is the degree of vertex v ∈ V(G) and Δ(G) is the maximum degree of G. A total labeling of graph G(V, E) is said to be local edge antimagic total labeling if a bijection f : V(G) ∪ E(G) → {1, 2, 3, …, |V(G)| + |E(G)|} such that for any two adjacent edges e 1 and e 2, wt (e 1) ≠ wt (e 2), where for e = uv ∈ G, wt (e) = f(u) + f(uv) + f(v). The local edge antimagic total labeling induces a proper edge coloring of G if each edge e is assigned the color wt (e). The edge local antimagic chromatic number of G denoted by γelat (G), is the minimum number of distinct color induced by edge weights over all local antimagic total labeling of G. In this paper, we determined the edge local antimagic chromatic number of Diamond Ladder graph, Pn ⊙ Pm Three Circular ladder graphht, and shack(F 2, v, n).

Super local edge anti-magic total coloring of paths and its derivation

<p>Suppose <em>G</em>(<em>V,E</em>) be a connected simple graph and suppose <em>u,v,x</em> be vertices of graph <em>G</em>. A bijection <em>f</em> : <em>V</em> ∪ <em>E</em> → {1,2,3,...,|<em>V</em> (<em>G</em>)| + |<em>E</em>(<em>G</em>)|} is called super local edge antimagic total labeling if for any adjacent edges <em>uv</em> and <em>vx</em>, <em>w</em>(<em>uv</em>) 6= <em>w</em>(<em>vx</em>), which <em>w</em>(<em>uv</em>) = <em>f</em>(<em>u</em>)+<em>f</em>(<em>uv</em>)+<em>f</em>(<em>v</em>) for every vertex <em>u,v,x</em> in <em>G</em>, and <em>f</em>(<em>u</em>) < <em>f</em>(<em>e</em>) for every vertex <em>u</em> and edge <em>e</em> ∈ <em>E</em>(<em>G</em>). Let γ(<em>G</em>) is the chromatic number of edge coloring of a graph <em>G</em>. By giving <em>G</em> a labeling of <em>f</em>, we denotes the minimum weight of edges needed in <em>G</em> as γ<em>leat</em>(<em>G</em>). If every labels for vertices is smaller than its edges, then it is be considered γ<em>sleat</em>(<em>G</em>). In this study, we proved the γ sleat of paths and its derivation.</p>

Computing Edge-Weight Bounds of Antimagic Labeling on a Class of Trees

Graph labeling has wide applications in the field of computer science, such as coding theory, cryptography, software testing, database management systems, computer architecture, and networking. The computers connected in a network can now be converted in a graph and labels assigned to the graph so formed will help to regulate bandwidth, data traffic, in coding and decoding signals. Let A = (V(Λ), E(Λ)) beagraphwith|V(Λ)| = m and|V(Λ)| = n.Abijection from ζ : V(Λ)∪E(Λ) → {1, 2, 3, ⋯,m + n} is called (a, d)-edge antimagic total labeling if the edge-weights ζ(x) + ζ(xy) + ζ(y) for each xy ∈ E(Λ) form a sequence of consecutive positive integers with minimum edge-weight a and common difference d. In addition, it is called super (a, d)-edge antimagic total labeling if vertices receive the smallest labels. Enomoto et al. (2000) proposed the conjecture that every tree admits super (a, 0)-EAT labeling. In this note, bounds of the minimum and maximum edge-weights for super (a, d)-EAT labeling on the more generalized class of subdivided caterpillars are obtained. Moreover, we have investigated the existence of super (a, d)EAT labeling for the validation of the obtained bounds and the partial support of the aforesaid conjecture, where d ∈ {0, 1, 2}. In fact, the obtained results are a general extension of the results Akhlaq et al. [Utiltas Mathematica, 98 (2015), 227-249].

On super (a, d)-edge-antimagic total labeling of Möbius ladder

A Möbius ladder is a simple graph obtained by introducing a twist in a prism graph. A Möbius ladder which has n pairs vertices is denoted by Mn. A graph G is called (a, d)-edge-antimagic total if there exists a bijection f from V (G) ∪ E (G) to {1, 2, …, |V (G) + E (G)|} such that the edge-weights, wf (uv) = f (u) + f (uv) + f (v), uv ∈ E (G), forms an arithmetic sequence with the first term a and common difference d. Further, it called super if f (V) = {1, 2, …, |V (G)|}. In this paper we proved that Mn is super (a, d)-edge-antimagic total with 0 ≤ d ≤ 2. Further, we showed that for every even n, Mn is not (a, 0)-edge-antimagic total.

Super local edge antimagic total coloring of

In this paper, we consider that all graphs are finite, simple and connected. Let G(V, E) be a graph of vertex set V and edge set E. A bijection is called a local edge antimagic labeling if for any two adjacent edges e1 and e2, , where for . Thus, any local edge antimagic labeling induces a proper edge coloring of G if each edge e is assigned the color w(e). It is considered to be a super local edge antimagic total coloring, if the smallest labels appear in the vertices. The super local edge antimagic chromatic number, denoted by γleat(G), is the minimum number of colors taken over all colorings induced by super local edge antimagic total labelings of G. In this paper we initiate to study the existence of super local edge antimagic total coloring of comb product of graphs. We also analyse the lower bound of its local edge antimagic chromatic number. It is proved that . Furthermore we have determine exact value local edge antimagic coloring of and .

Edge Antimagic Total Labeling on Two Copies of Path

A graph G = (V(G), E(G)) denotes the vertex set and the edge set, respectively. A (p,q)-graph G is a graph such that |V(G) | = p and |E(G) | = q. Graph of order p and size q is called (a,d)-edge-anti magic total if there exists a bijection f : V(G) U E(G)→ {1,2,..., p + q} such that the edge weights w(u,v) = f(u) + f(uv) + f(v) form an arithmetic sequence {a, a + d, a + 2d,...,a + (q – 1)d} with the first term a and common difference d. Two copies of path is disjoint union of two path graph with same order (Pn∪Pn) denoted by 2Pn. In this paper we construct the (a,d)-edge-anti magic total labeling in two copies of path for some differences d.

Super (a, d)-edge-antimagic total labelings of complete bipartite graphs

An (a, d)-edge-antimagic total labeling of a graph G is a bijection f from V(G) ∪ E(G) onto {1, 2,…,|V(G)| + |E(G)|} with the property that the edge-weight set {f(x) + f(xy) + f(y) | xy ∈ E(G)} is equal to {a, a + d, a + 2d,...,a + (|E(G)| − 1)d} for two integers a > 0 and d ⩾ 0. An (a, d)-edge-antimagic total labeling is called super if the smallest possible labels appear on the vertices. In this paper, we completely settle the problem of the super (a, d)-edge-antimagic total labeling of the complete bipartite graph Km,n and obtain the following results: the graph Km,n has a super (a, d)-edge-antimagic total labeling if and only if either (i) m = 1, n = 1, and d ⩾ 0, or (ii) m = 1, n ⩾ 2 (or n = 1 and m ⩾ 2), and d ∈ {0, 1, 2}, or (iii) m = 1, n = 2 (or n = 1 and m = 2), and d = 3, or (iv) m, n ⩾ 2, and d = 1.

Super [formula omitted]-edge antimagic total labeling of a subclass of trees

A graph labeling is a mapping that assigns numbers to graph elements. The domain can be the set of all vertices, the set of all edges or the set of all vertices and edges. A labeling in which domain is the set of vertices and edges is called a total labeling. For a graph G with the vertex set V(G) and the edge set E(G), a total labeling f:V(G)∪E(G)→{1,2,3,…,|V(G)|+|E(G)|} is called an (a,d)-edge antimagic total labeling if the set of edge weights {f(x)+f(xy)+f(y):xy∈E(G)} forms an arithmetic progression with initial term a and common difference d. An (a,d)-edge antimagic total labeling is called a super(a,d)-edge antimagic total labeling if the smallest labels are assigned to the vertices. In this paper, we investigate the super(a,d)-edge-antimagic total labeling of a subclass of trees called subdivided stars for all possible values of d, mainly d=1,3.

Edge Antimagic Total Labeling of Isomorphic Copies of Subdivided Stars

Enomoto, Llado, Nakamigawa and Ringel defined the concept of a super $(a,0)$-edge-antimagic total labeling and proposed the conjecture that every tree is a super $(a,0)$-edge-antimagic total labeling. In the support of this conjecture, the present paper deals with different results on antimagicness of isomorphic copies of subdivided stars.

SUPER EDGE ANTI-MAGIC VERTEX LABELING AND SUPER EDGE ANTI-MAGIC TOTAL LABELING OF A CYCLE WITH ZIG-ZAG CHORDS

In this paper, we show that super edge anti-magic vertex labeling and super edge anti-magic total labeling of cycles by adding (n-3) zig-zag chords.

Super (a, d)-edge antimagic total labelings of friendship and generalized friendship graphs

An (a, d)-edge-antimagic total labeling of a graph G with p vertices and q edges is a bijection f from the set of all vertices and edges to the set of positive integers {1,2,3,…,p+q} such that all the edge-weights w(uv)=f(u)+f(v)+f(uv); uv∈E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called a super (a, d)-edge-antimagic total labeling ((a, d)-SEAMT labeling) if f(V(G))={1,2,3,…,p}. In this paper we investigate the existence of super (a, d)-edge antimagic total labeling for friendship graphs and generalized friendship graphs.

Super [formula omitted]-EAT labeling of subdivided stars

Kotzig and Rosa conjectured that every tree admits an edge-magic total labeling. Enomoto et al. proposed the conjecture that every tree is a super (a,0)-edge-antimagic total graph. In this paper, we formulate a super (a,d)-edge-antimagic total labeling on the subdivided star T(n,n,n+4,n+4,n5,n6...,nr) for d∈{0,1,2}, where r≥5, np=2p−4(n+3)+1, 5≤p≤r and n≥3 is odd.

Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph

Let G be a simple graph of order p and size q. Graph G is called an (a,d)-edge-antimagic totalifthereexistabijectionf :V(G)∪E(G)→{1,2,...,p+q}suchthattheedge-weights,w(uv)= f(u)+f(v)+f(uv); u, v ∈ V (G), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge antimagic total properties of connected of Ferris Wheel F Wm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all feasible d. Key Words : (a, d)-edge antimagic vertex labeling, super (a, d)-edge antimagic total labeling, Ferris Wheel graph FWm,n.

On Super Edge-Antimagicness of Circulant Graphs

A labeling of a graph is a mapping that carries some sets of graph elements into numbers (usually the positive integers). An $$(a,d)$$(a,d)-edge-antimagic total labeling of a graph $$G(V,E)$$G(V,E) is a one-to-one mapping $$f$$f from $$V(G)\cup E(G)$$V(G)?E(G) onto the set $$\{1,2,\dots , |V(G)|+|E(G)|\}$${1,2,?,|V(G)|+|E(G)|}, such that the set of all the edge-weights, $$wt_f (uv) = f(u) +f(uv)+f(v)$$wtf(uv)=f(u)+f(uv)+f(v), $$uv\in E(G)$$uv?E(G), forms an arithmetic sequence starting from $$a$$a and having a common difference $$d$$d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we study the existence of such labelings for circulant graphs.

On Edge Antimagic Total Labeling and Arithmetic Progression

Abstract- An edge magic total labeling of graph with p vertices and q edges is a bijection from the set of vertices and edges to 1, 2, 3,…,p+qsuch that for every edge the sum of the label of the edges and the label of its two end vertices are constant . And if the sum is distinct it is said to be an edge antimagic total labeling. In this paper, we exhibit edge antimagic total labeling on graph structure for various arithmetic progression.