The Minimum Edge Covering Energy of a Graph

In this paper, we introduce a new kind of graph energy, the minimum edge covering energy, ECE(G). It depends both on the underlying graph G, and on its particular minimum edge covering CE. Upper and lower bounds for ECE(G) are established. The minimum edge covering energy and some of the coefficients of the polynomial of well-known families of graphs like Star, Path and Cycle Graphs are computed

On Edge Covering Chain of a Graph

Abstract- In the study of domination in graphs, relationships between the concepts of maximal independent sets, minimal dominating sets and maximal irredundant sets are used to establish what is known as domination chain of parameters. 0 ir(G)  (G)  i(G)   (G)  (G)  IR(G) In this paper, starting from the concept of edge cover, six graph theoretic parameters are introduced which obey a chain of inequalities, called as the edge covering chain of the graph G

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 .

Some Zero-One Linear Programming Reformulations for the Maximum Clique Problem

Many combinatorial optimization problems can be expressed in terms of zero-one linear programs. For the maximum clique problem the so-called edge reformulation is applied most commonly. Two less frequently used LP equivalents are the independent set and edge covering set reformulations. The number of the constraints (as a function of the number of vertices of the ground graph) is asymptotically quadratic in the edge and the edge covering set LP reformulations and it is exponential in the independent set reformulation, respectively. F. D. Croce and R. Tadei proposed an approach in which the number of the constraints is equal to the number of the vertices. In this paper we are looking for possible tighter variants of these linear programs.

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.

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) )