Let G = (V (G), E(G)) be a simple graph and H be a subgraph of G. G admits anH-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection λ : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G)|+ |E(G)|} such that for all subgraphs H ′ isomorphic to H, the H ′ weights wt(H ) = ∑

Let be a connected graph with vertex set and edge . The bijective function is said to labeling of where the associated weight for If every has different weight, called an antimagic labeling. A path in vertex-labeled , two edges satisfies rainbow path. if vertices there exists Graph admits coloring, we assign each color smallest number colors induced from all weights connection denoted by In thi...

A Cayley digraph is a digraph constructed from a group Γ and a generating subset S of Γ. It is denoted by CayD(Γ, S). In this paper, we prove for any finite group Γ and a generating subset S of Γ, that CayD(Γ, S) admits a super vertex (a, d)-antimagic labeling depending on d and |S|. We provide algorithms for constructing the labelings.

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection ƒ : E ? {1, 2, 3, ..., q} is called local antimagic labeling if for all uv ? we have w(u) ? w(v), the weight ?e?E(u) f(e) where E(u) set edges incident to u. has labeling. The chromatic number ?la(G) defined minimum colors taken over colorings induced by labelings G. In this paper, determine some wheel relat...

Given a graph G with vertex set V(G) and edge E(G), for the bijective function f(V(G))?{1,2,?,|V(G)|}, associated weight of an xy?E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, called edge-antimagic labeling. A path P in vertex-labeled said to be rainbow x?y if every two xy,x?y??E(P) it satisfies w(xy)?w(x?y?). The antimagic labeling there exists vertices x,y?V(G)...

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...

Let G = G(V, E) be a finite simple undirected graph with vertex set V and edge set E, where |E| and |V | are the number of edges and vertices on G. An (a, d)-edge antimagic vertex ((a, d)-EAV) labeling is a one-toone mapping f from V (G) onto {1, 2, . . . , |V |} with the property that for every edge xy ∈ E, the edge-weight set is equal to {f(x) + f(y) : x, y ∈ V } = {a, a+ d, a+2d, . . . , a+(...