A vertex-magic total labeling of a graph G(V; E) is a one-to-one map from E ∪V onto the integers {1; 2; : : : ; |E|+ |V |} such that (x) + ∑ (xy); where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite di9erent from the conjecture...

A graph G = (V (G), E(G)) admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is H-magic if there exists a bijection f : V (G)∪E(G)→ {1, 2, 3, . . . , |V (G)∪E(G)|} such that for every subgraph H ′ of G isomorphic to H, ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e) is constant. Then G is H-supermagic if f(V (G)) = {1, 2, 3, . . . , |V (G)|}. Let {Gi}i=1 be a fi...

Let G be a graph and f : V (G) → {1, 2, 3, . . . , p+ q} be an injection. For each edge e = uv and an integer m ≥ 2, the induced Smarandachely edge m-labeling f∗ S is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, . . . , p+ q}. Particularly, in the case of m = 2, we know that f ∗(e) =    f(u)+f(v) ...

For every h ∈ N, a graph G with the vertex set V (G) and the edge set E(G) is said to be h-magic if there exists a labeling l : E(G) → Zh\{0} such that the induced vertex labeling s : V (G) → Zh, defined by s(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is zero, we say that G admits a zero-sum h-magic labeling. The null set of a graph G, denoted by N(G), is the set of all natural ...

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...

ARTICLE INFO An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p+ q} such that for every copy H in the decomposition, ∑

A graph G is said to be A-magic if there is a labeling l : E(G) −→ A − {0} such that for each vertex v, the sum of the labels of the edges incident with v are all equal to the same constant; that is, l+(v) = c for some fixed c ∈ A. In general, a graph G may admit more than one labeling to become A-magic; for example, if |A| > 2 and l : E(G) −→ A − {0} is a magic labeling of G with sum c, then l...