As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. We define a 1-vertex-magic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2, . . . , v with the property that there is a constant k such that at any vertex x, ∑ y∈N(x) f(y) = ...

Graphs that have the properties of odd harmonious labeling are graphs. The research objective this paper is to obtain on layered graph C(x,y) and D(x,y). used in a qualitative method. flow consists data collection, processing, analysis. collection stage constructing definition new class graph, processing vertex edge labeling, analysis theorem proving it. results show D(x,y) fulfill labeling. Su...

The double-stranded DNA (dsDNA) virus PRD1 carries its genome in a membrane surrounded by an icosahedral protein shell. The shell contains 240 copies of the trimeric P3 protein arranged with a pseudo T = 25 triangulation that is reminiscent of the mammalian adenovirus. DNA packaging and infection are believed to occur through the vertices of the particle. We have used immunolabeling to define t...

Let G = (V,E) be a graph of order n and size e. An (a, d)-vertexantimagic total labeling is a bijection α from V (G) ∪ E(G) onto the set of consecutive integers {1, 2, . . . , n + e}, such that the vertex-weights form an arithmetic progression with the initial term a and the common difference d. The vertex-weight of a vertex x is the sum of values α(xy) assigned to all edges xy incident to the ...

A graph G of size q is graceful if there exists an injective function f : V (G) → {0, 1, . . . , q} such that each edge uv of G is labeled |f(u)− f(v)| and the resulting edge labels are distinct. Also, a (p, q) graph G with q ≥ p is harmonious if there exists an injective function f : V (G) → Zq such that each edge uv of G is labeled f(u)+f(v) (mod q) and the resulting edge labels are distinct,...

In this paper, we are studying vertex-magic total labelings (VMTLs) of simple graphs. By now much is known about methods for constructing VMTLs for regular graphs. Here we are studying non-regular graphs. We show how to construct labelings for several families of non-regular graphs, including graphs formed as the disjoint union of two other graphs already possessing VMTLs. We focus on condition...

A vertex-magic total labeling of a graph G(V; E) is a one-to-one map from E ∪V onto the integers {1; 2; : : : ; |E|+ |V |} such that (x) + ∑ (xy); where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite di9erent from the conjecture...

In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated graph. We exploit the transformation proposed by C...

In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated graph. We exploit the transformation proposed by C...