Pelabelan Selimut Bintang Ajaib Super Pada Graf Bintang

Let be a simple graph. An edge covering of is a family of subgraphs such that each edge of graph belongs to at least one of the , subgraphs. If each is isomorphic with the given graph , then it is said that contains a covering. The graph G contains a covering and the bijectif function is said an the magic labeling of a graph G if for each subgraph of is isomorphic to , so that is a constant. It is said that the graph G has a super magic if in this case, the graph G which can be labeled with magic is called the covering graph magic. A star graph with n points is a graph with points and sides, where point is degree and the other point has degree denoted by . This study aims to determine the presence of covering labeling for the super-magic star on the star graph. The research methodology is literature study. The results show that the star graph for has magic covering labeling with magic constants for all covering is and the super-magic covering labeling with magic constants for all covering is .

Medians are Below Joins in Semimodular Lattices of Breadth 2

Let L be a lattice of finite length and let d denote the minimum path length metric on the covering graph of L. For any $\xi =(x_{1},\dots ,x_{k})\in L^{k}$ ξ = ( x 1 , … , x k ) ∈ L k , an element y belonging to L is called a median of ξ if the sum d(y,x1) + ⋯ + d(y,xk) is minimal. The lattice L satisfies the c1-median property if, for any $\xi =(x_{1},\dots ,x_{k})\in L^{k}$ ξ = ( x 1 , … , x k ) ∈ L k and for any median y of ξ, $y\leq x_{1}\vee \dots \vee x_{k}$ y ≤ x 1 ∨ ⋯ ∨ x k . Our main theorem asserts that if L is an upper semimodular lattice of finite length and the breadth of L is less than or equal to 2, then L satisfies the c1-median property. Also, we give a construction that yields semimodular lattices, and we use a particular case of this construction to prove that our theorem is sharp in the sense that 2 cannot be replaced by 3.

H-Coverings of Path-Amalgamated Ladders and Fans

Let G be a connected, simple graph with finite vertices v and edges e . A family G 1 , G 2 , … , G p ⊂ G of subgraphs such that for all e ∈ E , e ∈ G l , for some l , l = 1,2 , … , p is an edge-covering of G . If G l ≅ ℍ , ∀ l , then G has an ℍ -covering. Graph G with ℍ -covering is an a d , d - ℍ -antimagic if ψ : V G ∪ E G ⟶ 1,2 , … , v + e a bijection exists and the sum over all vertex-weights and edge-weights of ℍ forms a set a d , a d + d , … , a d + p − 1 d . The labeling ψ is super for ψ V G = 1,2,3 , … , v and graph G is ℍ -supermagic for d = 0 . This manuscript proves results about super ℍ -antimagic labeling of path amalgamation of ladders and fans for several differences.

Enumerating Abelian Typical Cube-Free Fold Coverings of a Circulant Graph

Enumerating the isomorphism or equivalence classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory. A covering projection p from a Cayley graph Cay(Γ, X) onto another Cayley graph Cay(Q, Y) is called typical if the function p : Γ → Q on the vertex sets is a group epimorphism. A typical covering is called abelian (or circulant, respectively) if its covering graph is a Cayley graph on an abelian (or a cyclic, respectively) group. Recently, the equivalence classes of connected abelian typical prime-fold coverings of a circulant graph are enumerated. As a continuation of this work, we enumerate the equivalence classes of connected abelian typical cube-free fold coverings of a circulant graph.

Covering Graphs, Magnetic Spectral Gaps and Applications to Polymers and Nanoribbons

In this article, we analyze the spectrum of discrete magnetic Laplacians (DML) on an infinite covering graph G ˜ → G = G ˜ / Γ with (Abelian) lattice group Γ and periodic magnetic potential β ˜ . We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on β ˜ . The magnetic potential can be interpreted as a control parameter for the spectral bands and gaps. We apply these results to describe the spectral band/gap structure of polymers (polyacetylene) and nanoribbons in the presence of a constant magnetic field.

PELABELAN SELIMUT AJAIB SUPER PADA GRAF LINTASAN

Let 𝐺 = (𝑉, 𝐸) be a simple graph. An edge covering of 𝐺 is a family of subgraphs 𝐻1 , … , 𝐻𝑘 such that each edge of 𝐸(𝐺) belongs to at least one of the subgraphs 𝐻𝑖 , 1 ≤ 𝑖 ≤ 𝑘. If every 𝐻𝑖 is isomorphic to a given graph 𝐻, then the graph 𝐺 admits an 𝐻 − covering. Let 𝐺 be a containing a covering 𝐻, and 𝑓 the bijectif function 𝑓: (𝑉 ∪ 𝐸) → {1,2,3, … , |𝑉| + |𝐸|} is said an 𝐻 −magic labeling of 𝐺 if for every subgraph 𝐻 ′ = (𝑉 ′ ,𝐸 ′ ) of 𝐺 isomorphic to 𝐻, is obtained that ∑ 𝑓(𝑉) + ∑ 𝑓(𝐸) 𝑒∈𝐸(𝐻′ 𝑣∈𝑉(𝐻 ) ′ ) is constant. 𝐺 is said to be 𝐻 −super magic if 𝑓(𝑉) = {1, 2, 3, … , |𝑉|}. In this case, the graph 𝐺 which can be labeled with 𝐻-magic is called the covering graph 𝐻 −magic. The sum of all vertex labels and all edge labels on the covering 𝐻 − super magic then obtained constant magic is denoted by ∑ 𝑓(𝐻). The duplication graph 2 of graph 𝐷2 (𝐺) is a graph obtained from two copies of graph 𝐺, called 𝐺 and 𝐺 ′ , with connecting each respectively vertex 𝑣 in 𝐺 with the vertexs immediate neighboring of 𝑣 ′ in 𝐺 ′ . The purpose of this study is to obtain a covering super magic labeling for of 𝐷2 (𝑃𝑚) on (𝐷2 (𝑃𝑛 )) for 𝑛 ≥ 4 and 3 ≤ 𝑚 ≤ 𝑛 − 1. In this paper, we have showed that duplication path graph (𝐷2 (𝑃𝑛 )) has 𝐷2 (𝑃𝑚) covering super magic labeling for 𝑛 ≥ 4 and 3 ≤ 𝑚 ≤ 𝑛 − 1 with constant magic for all covering is ∑ 𝑓(𝐷2 (𝑃𝑚) (𝑠) ) = ∑ 𝑓(𝐷2 (𝑃𝑚) (𝑠+1) )

On Pentavalent Arc-Transitive Graphs

In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph Γ is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are ℤ3, ℤ5 or a subgroup of [Formula: see text].

On 3-arc-transitive covers of the dodecahedron graph

In this paper, the following problem is considered: does there exist a t-arc-transitive regular covering graph of an s-arc-transitive graph for positive integers t greater than s? In order to answer this question, we classify all arc-transitive cyclic regular covers of the dodecahedron graph. Two infinite families of 3-arc-transitive abelian covering graphs are given, which give more specific examples that for an s-arc-transitive graph there exist (s+1)-arc-transitive covering graphs.