Vertex-Magic H-Multiple Labeling Essay
For each q, 0 ⩽ q ⩽ m-1, the labeling π γ, a vertex magic total labeling of G with magic constant n -q. The attentive reader will recognize that taking q, the upper bound for h in the abstract, while taking q, m yields the lower bound. If q, 0, then π γ is indeed the vertices with the smallest possible. For a graph GV,E, an injective map f from V∪E to the set 1,2,3,⋯,ν ε is a vertex-magic total labeling if there is a constant k, such that for each vertex v∈V, fv Σf uv, h where the. 2.1 - Magic Total Labels. Another magical total labeling that has also been studied is a kind where the sum of the labels of all edges adjacent to each vertex v, plus the label of v itself, is constant. This labeling was introduced by MacDougall et al. and was called vertex-magic total labeling. 8An 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, fx, f xy, fy, k , for. An a,d -edge-antimagic total labeling of a graph, with p vertices and q edges, is a one-to-one mapping that brings the vertices and edges into the,pq, such that the sums of. In this paper, we study some basic properties of such labelings and establish magical E-super vertex labels for some families of graphs. The main focus of this article is on the E-super vertex magic of H mn and some necessary conditions for a graph to be E-super vertex magic. A vertex-magic total labeling VMTL on a graph with v vertices and e edges is a one-to-one mapping from the vertices and edges to the 2, v, e such that the sum of the label. Application of Fuzzy Vertex Magic Total Labeling Graph. Described the current passing through the transformer shown in Figure 4. Consider the transformer τ i where i, 1, 2, n represents the vertex. The transformer dividing the current from τ i to τ j is taken as an edge between the vertex, An 𝑎, 𝑠 - vertex antimagic edge labeling or a 𝑎, 𝑠 -VAE labeling, in short 𝐺 is a bijective mapping from the edge set 𝐸 𝐺 from a graph 𝐺 to the set of A vertex-magic total labeling of a graph with v vertices and e edges is defined as a one-to-one map where the vertices and edges are brought to the, v, e with the property that the sum. A vertex magic total labeling is an assignment of the integers, 3. m, n to the vertices and edges of G, such that at each vertex the vertex label and the edge labels are incident. A magic vertex label on a graph with v-vertices and e-edges is a one-to-one map that takes the vertices and edges on the, 2 v, e with the property that the sum of the label is.