An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all edges incident $x$. The chromatic number $G$, denoted by $\chi_{la}(G)$, minimum distinct labels labelings $G$. In this...

Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V (G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V (G) to A such that the weights of ...

A graph G = (V (G), E(G)) admits an H -covering if every edge in E belongs to a subgraph of G isomorphic to H . A graph G admitting an H -covering is called (a, d) -H -antimagic if there is a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that, for all subgraphs H ′ of G isomorphic to H , the H -weights, wtf (H ′) = ∑ v∈V (H′) f(v)+ ∑ e∈E(H′) f(e), constitute an arithmetic p...

A graph G = (V,E) is called antimagic if there exists a bijection from the set of edges to the integers 1, . . . , |E| such that all |V | vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. According to Ringel's Conjecture in [4], every simple connected graph, other than K2, is antimagic. In [5], Hefetz proved that every graph on n ...

A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithm...

An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it Bijection f : E ? {1, … ,|E|} such that for any pair adjacent vertices x and y, f+(x) ? f+(y), where the induced vertex label ?f(e), with e ranging over all edges incident x. The chromatic number G, denoted by ?la(G), minimum distinct labels labelings G. In this paper, we first show d-leg spider has d + 1 ? ?la...