Many structural models in chemistry, biology, computer science, sociology, and operations
research can be analyzed using graph theory. Some examples of these structure models are …

For a simple graph $ G $, a vertex labeling $\phi: V (G)\rightarrow\{1, 2,\ldots, k\} $ is called $
k $-labeling. The weight of an edge $ xy $ in $ G $, written $ w_ {\phi}(xy) $, is the sum of the …

Let G be a simple graph. A function ϕ: V (G)→{1, 2,..., k} a vertex k-labeling which assigns
labels to the vertices of G. For any edge xy in G, we define the weight of this edge as wϕ …

After the Chartrand definition of graph labeling, since 1988 many graph families have been
labeled through mathematical techniques. A basic approach in those labelings was to find a …