<p>Among the most studied graph labelings we have varieties called alpha and edge-magic. Even when their definitions seem completely different, these are related. A graceful labeling of a bipartite is an α-labeling if smaller labels assigned to vertices same stable set. An edge-magic size <em>n</em> said be <em>b</em>-edge consecutive its edges labeled with integer...

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 vertex u is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an antimagic labeling. Hartsfield and Ringel conject...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

A Γ -magic rectangle set MRSΓ (a, b; c) of order abc is a collection of c arrays (a× b) whose entries are elements of group Γ , each appearing once, with all row sums in every rectangle equal to a constant ω ∈ Γ and all column sums in every rectangle equal to a constant δ ∈ Γ . In the paper we show that if a and b are both even then MRSΓ (a, b; c) exists for any Abelian group Γ of order abc. Fu...

In this paper, we have proved edge-magic total labeling of cycles with P3 chords.

Let A be an abelian group. An A-magic of a graph G = (V, E) is a labeling l : E(G) → A \ {0} such that the sum of the labels of the edges incident with u ∈ V is a constant, where 0 is the identity element of the group A. In this paper, we will show that some classes of graphs are A-magic for all abelian group A of even order other than 2. Also, we prove that product and composition of A-magic g...

The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.