An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, . . . , q} such that the vertex sums are pairwise distinct, where the vertex sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an anti-magic labeling. Hartsfield and Ringel c...

Consider a graph G with |V (G)| = p and |E(G)| q let f : V (G) → {k, k + 1, 2, . − 1}} be an injective function. The induced edge labeling ∗ for vertex is defined by (e) all e uv ∈ E(G) bijective. If f(V (G)) ∪ {f E(G)} , 1}, then called k-super cube root mean labeling. such exists, graph. In this paper, I introduce prove the existence of to graphs viz., triangular snake Tn, double D(Tn), Quadr...

For a given graph G, let V be the number of vertices and E be the number of edges. Consider a labeling of the vertices and edges which is a one-to-one mapping of the set of integers {1, 2, . . . , V + E} onto the vertices and edges of the graph, with the property that for every vertex the sum of the labels assigned to that vertex and all edges incident with it is some constant k. Although work ...

Let G = (V (G), E(G), F (G)) be a simple, finite, connected, plane graph with the vertex set V (G), the edge set E(G) and the face set F (G). A labeling of type (1, 1, 1) assigns labels from the set {1, 2, . . . , |V (G)|+ |E(G)| + |F (G)|} to the vertices, edges and faces of a plane graph G, such that each vertex, edge and face receives exactly one label and each number is used exactly once as...

Let $$G = (V,E)$$ be a connected simple graph of order p and size q. A G is called local antimagic if admits labeling. bijection $$f \colon E \to \{1,2,\ldots,q\}$$ labeling for any two adjacent vertices $$u$$ $$v$$ , we have $$f^+(u) \ne f^+(v)$$ where \sum_{e\in E(u)} f(e)$$ $$E(u)$$ the set edges incident to . Thus, induces proper vertex coloring assigned color $$f^+(v)$$ The chromatic numbe...

Let G = (V,E) be a (p, q)-graph of order p and size q and f be a bijection from the set V ∪ E to the set of the first p + q natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say f is an (a, d)-vertex-antimagic total labeling if the vertex-weights form an arithmetic progression with the initial term a and the common difference d. Such a labe...

Context. The gamma-ray binary LS I +61303 is a well-established source from centimeter radio up to very high energy (VHE; E > 100 GeV). The broadband emission shows a periodicity of ∼26.5 days, coincident with the orbital period. A longer (super-orbital) period of 1667 ± 8 days was proposed from radio variability and confirmed using optical and high-energy (HE; E ¿ 100 MeV) gamma-ray observatio...

In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which ha...