Magic Labeling Research Articles

(S,d)Magic Labeling of Some Cycle Related Graphs

(S,d)Magic Labeling of Some Cycle Related Graphs

How to Construct Super Edge-Magic Total Labeling of Theta Graph θ(2,b,c)

This research study and provide the property of super edge-magic total labelings of theta graph. Edge magic labeling on a graph is an injective function from to a subset of integers { } with the property that there is a positive integer such as for each . An edge-magic labeling is called super edge-magic total labeling if it satisfies . A graph is called (super) edge-magic total if it admits some (super) edge-magic total labeling. A theta graph is constructed by embedding the endpoints of three paths of length consecutive such that there are two vertices of degree three and the other of degree two. This study gave some conditions for such a super edge-magic total of theta graph. Based on this condition, this paper introduce some algorithms to apply and develop super edge-magic total labeling from some previous theta graphs.

Distance magic labelings of Cartesian products of cycles

A graph of order n is distance magic if it admits a bijective labeling of its vertices with integers from 1 to n such that each vertex has the same sum of the labels of its neighbors. In this paper we classify all distance magic Cartesian products of two cycles, thereby correcting an error in a widely cited paper from 2004. Additionally, we show that each distance magic labeling of a Cartesian product of cycles is determined by a pair or quadruple of suitable sequences, thus obtaining a complete characterization of all distance magic labelings of these graphs. We also determine a lower bound on the number of all distance magic labelings of Cm□C2m with m≥3 odd.

Distance Magic Labeling of Corona Product of Graphs

Distance Magic Labeling of Corona Product of Graphs

On D-distance (anti)magic labelings of shadow graph of some graphs

On D-distance (anti)magic labelings of shadow graph of some graphs

Group vertex magic labeling of some special graphs

For any additive abelian group $A$. Let $\mu$ be an element of $A$, a graph $G=(V,E)$ is said to be $A$-vertex magic graph if there exist a labeling function $f:V(G)\rightarrow A\setminus\{0\}$ such that $\omega(v)=\sum_{u\in N(v)} f(u)=\mu$ for any vertex $v$ of $G$, where $N(v)$ is the set of the open neighborhood of $v$. In this paper, we prove that the graphs such as wheel, Corona $C_{n}\odot mk$, subdivision of ladder and $t$-fold wheel for $t\neq n$ nor $n-2$ are $A$-vertex magic graphs. Also we prove that the subdivide wheel, helm and closed helm are $Z_{k}$-vertex magic graphs. However we prove that the triangular book and $t$-fold wheel for $t=n,n-2$ are group vertex magic graphs.

Graphical image of Trisomy Ultrascan related Total edge magic labelling

INTRODUCTION: The goal of this research is to investigate child syndromes at the overall level using total edge magic labelling. luckily discussed with chromosomal diseases consisting of Down's syndrome, the syndrome of Edwards, and Patau syndrome.
 OBJECTIVES: Ultrasound is used to check for Patau's, Edwards, and Down syndrome between 11 and 14 weeks of pregnancy. These syndromes can be determined before the baby is born. The name for trisomy 21 or Down syndrome. Trisomy 18 or Edwards syndrome; trisomy 13 or Patau syndrome.
 METHODS: The ultrasound screen test was converted to a graphical image, and Total edge magic labelling was implemented. A bijection from VUE to the numbers, {1, 2, 3, … p+q} with the characteristic that each everybody uv Ɛ E, Γ(u)+ Γ(uv)+ Γ(v) = Ψ for some constant Ψ, is known as Total edge magic labelling.
 RESULTS: The results of this test will determine the baby’s type of trisomy. This study's impartial was to assess the efficacy of screening for 21, 18, and 13 trisomies at the 12-week mark in pregnancy.
 CONCLUSION: The intended audience of this paper is a man or woman with a chromosomal disorder who should know about the health of their ancestors. A couple can go for genetic counselling and then plan for a baby.

Distance magic labeling of join of graphs and big data analysis

Consider a simple graph G = 〈V, E〉 with n vertices. Define a function f from vertex set of G to set of integers 1, 2, …, n subject to the condition that there exists an integer k > 0 such that the sum of adjacent labels of each vertex in G is equal to k. In this paper, we prove that the graph K n - ⌊ n 2 ⌋ e has DML for all n ≥ 1, decomposition of distance magic graph K2n - {ne} into n ( n - 1 ) 2 edge distinct copies of C4 for all n ≥ 2 and DML of join of complete graphs gives unique mathematical model and it will be a useful model in big data analysis.

On Regular Distance Magic Graphs of Odd Order

Let G=(V,E) be a graph with n vertices. A bijection f:V→{1,2,…,n} is called a distance magic abeling f G if there exists an integer k such that ∑u∈N(v)f(u)=k for all v∈V, where N(v) is the set of all ertices adjacent to v. Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by ronček, Kovář, and Kovářová. In two recent papers, the existence of 4-regular and of (n−3)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar classification of all feasible odd orders of r-regular distance magic graphs when r=6,8,10,12. Even though some nonexistence proofs for small orders are done by brute force enumeration, all the existence proofs are constructive.

Cycle-Super Magic Labeling of Polyomino Linear and Zig-Zag Chains

A bijective function with domain union of vertex and edge set to a range natural numbers to onward count of vertices and edges of a graph. If there is a bijective function G, then G is called as a H-magic graph, along with the condition that every subgraph H’ from the original graph G, H’ is isomorphic to H and with the interesting fact that sum of all the values of vertices and edges is constant for all H’. This condition can be more advance and strict when the first order-numbers assigned to the vertices only and then this definitions is called as H-super magic. In this paper, we study some polyomino structures, including zig-zag and linear chains. We studied, C8-super magic labeling of zig-zag, linear chains and also the disjoint union of non-isomorphic copies of both chains.

Efficient Graph Network Using Total Magic Labeling and Its Applications

Cryptography is a pivotal application of graph theory in ensuring secure communication systems. Modern cryptography is deeply rooted in mathematical theory and computer science practices. It is widely recognized that encryption and decryption processes are primarily outcomes of mathematical research. Given the increasing importance of safeguarding secret information or messages from potential intruders, it is imperative to develop effective technical tools for this purpose. These intruders are often well-versed in the latest technological advancements that could breach security. To address this, our study focuses on the efficacious combinatorial technique of graph networks using efficient domination and total magic labeling. The introduction of a graph network based on total magic labeling can significantly influence the network’s performance. This research introduces a novel combinatorial method for encrypting and decrypting confidential numbers by leveraging an efficient dominant notion and labeled graph.

Group distance magic labeling of tetravalent circulant graphs

Let G=(V,E) be a finite simple graph of order n and let Γ be an abelian group of order n. A Γ-distance magic labeling of G is a bijection φ:V⟶Γ for which there exists γ∈Γ such that ∑x∈N(v)φ(x)=γ for any v∈V, where N(v) is the neighborhood of v. In this paper, we classify all connected tetravalent circulant graphs which admit a Γ-distance magic labeling for any given finite abelian group Γ.

On closed distance magic circulants of valency up to 5

Let Γ=(V,E) be a graph of order n. A closed distance magic labeling of Γ is a bijection ℓ:V→{1,2,…,n} for which there exists a positive integer r such that ∑x∈N[u]ℓ(x)=r for all vertices u∈V, where N[u] is the closed neighborhood of u. A graph is said to be closed distance magic if it admits a closed distance magic labeling.In this paper, we classify all connected closed distance magic circulants with valency at most 5, that is, Cayley graphs Cay(Zn;S) where |S|≤5, S=−S, 0∉S and S generates Zn.

On (F, H)-simultaneously-magic labelings of graphs

A simple graph G ( V , E ) admits an H -covering if every edge in G belongs to a subgraph of G isomorphic to H . In this case, G is called H -magic if there exists a bijective function f : V ∪ E → {1, 2, …, | V |+| E |} , such that for every subgraph H ′ of G isomorphic to H , w t f ( H ′) = Σ v ∈ V ( H ′) f ( v )+ Σ e ∈ E ( H ′) f ( e ) is constant. Moreover, G is called H -supermagic if f : V ( G )→{1, 2, …, | V |} . This paper generalizes the previous labeling by introducing the ( F , H ) -sim-(super) magic labeling. A graph admitting an F -covering and an H -covering is called ( F , H ) -sim-(super) magic if there exists a function f that is F -(super)magic and H -(super)magic at the same time. We consider such labelings for two product graphs: the join product and the Cartesian product. In particular, we establish a sufficient condition for the join product G + H to be ( K 2 + H , 2 K 2 + H ) -sim-supermagic and show that the Cartesian product G × K 2 is ( C 4 , H ) -sim-supermagic, for H isomorphic to a ladder or an even cycle. Moreover, we also present a connection between an α -labeling of a tree T and a ( C 4 , C 6 ) -sim-supermagic labeling of the Cartesian product T × K 2 .

Pelabelan Jarak Tak Teratur Titik Pada Graf Persahabatan Lengkap Diperumum

Graph labeling is the labeling of graph elements such as vertex, edge and both. distance vertex irregular labeling is a type of labeling resulting from the development of distance magic labeling and (a, b)-distance anti-magic labeling. Let , be a simple graph. The distance vertex irregular labeling of is a vertex labeling so that the weight of each vertex is different. The weight of is calculated based on the sum of vertices label in the set of neighboring vertex , namely Distance vertex irregularity strength of , denoted as d , is the smallest value of the largest label so that has a distance vertex irregular labeling. This study aims to construct a generalized complete friendship graph , determine the labeling function, determine the distance vertex irregularity strength then formulate and prove the theorem resulting from the labeling. The object of this research is to label each vertex on a generalized complete friendship graph. This research method is a literature study obtained through various sources. Based on the research results, it is known that the graph has distance vertex irregular labeling. For an integer m and n, , the labeling function of is and . Distance vertex irregularity strength of generalized complete friendship graph is .

Characterize group distance magic labeling of Cartesian product of two cycles

Given a graph G with vertex set V(G) and an abelian group Γ of order |V(G)|, a Γ-distance magic labeling of G is a bijection φ:V(G)⟶Γ with the property that there exists μ∈Γ such that ∑y∈N(x)φ(y)=μ for any x∈V(G), where N(x) is the neighborhood of x and μ is the magic constant of this labeling.Froncek showed that the Cartesian product Cm□Cn admits a Zmn-distance magic labeling if and only if 2|mn, and asked for the full characterization of the group Γ such that Cm□Cn admits a Γ-distance magic labeling. Recently, Cichacz, Dyrlaga and Froncek made some progress toward this problem, but the general case is still open.In this paper, we completely solve this problem. We also determine all μ∈Zmn such that there exists a Zmn-distance magic labeling of Cm□Cn with magic constant μ.

Distance magic labeling of the halved folded n-cube

Distance magic labeling of the halved folded n-cube

On magic distinct labellings of simple graphs

A magic labelling of a graph G with magic sum s is a labelling of the edges of G by nonnegative integers such that for each vertex v∈V, the sum of labels of all edges incident to v is equal to the same number s. Stanley gave remarkable results on magic labellings, but the distinct labelling case is much more complicated. We consider the complete construction of all magic labellings of a given graph G. The idea is illustrated in detail by dealing with three regular graphs and a non-regular graph. We give combinatorial proofs. The structure result was used to enumerate the corresponding magic distinct labellings. The idea can be carried out directly for graphs with no more than 9 edges.

Results on Hefty V4-Vertex Magic Graph Labeling

Let V4 be an abelian group under multiplication. Let g : E(G) →V4 −{1}. The vertex magic labeling on V4 is defined as the vertex labeling g∗ : V (G) →V4 such that ), where the product is taken over all edges uv of G incident at v is a constant. If the constant is 1, it becomes a Hefty V4-vertex magic labeling. A graph is said to be Hefty V4-magic graph if it admits a Hefty V4-vertex magic labeling. In this paper we investigate the Hefty V4-vertex magic labeling behaviour of graphs like Bipartite, Complete graph, Cayley graph etc.

Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials

In chemistry, Cyvin-Gutman enumerates Kekulé numbers for certain benzenoids and record it as A050446 on OEIS. This number is exactly the two variable array T(n,m) defined by the recursion T(n,m)=T(n,m−1)+∑k=0⌊n−12⌋T(2k,m−1)T(n−1−2k,m), where T(n,0)=T(0,m)=1 for all nonnegative integers m,n. Interestingly, this number also appeared in the context of weighted graphs, graph polytopes, magic labellings, and unit primitive matrices, studied by different authors. Several interesting conjectures were made on the OEIS. These conjectures are related to both the row and column generating function of T(n,m). In this paper, we give explicit formula of the column generating function, which is also the generating function F(n,x) studied by Bóna, Ju, and Yoshida. We also get trig function representations by using Chebyshev polynomials of the second kind. This allows us to prove all these conjectures.