For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic}  if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$  defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$  the group of integers modulo $k...

Acharya and Hegde have introduced the notion of strongly k-indexable graphs: A (p, q)-graph G is said to be strongly k-indexable if its vertices can be assigned distinct integers 0, 1, 2, ..., p − 1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices can be arranged as an arithmetic progression k, k+ 1, k + 2, ..., k + (q − 1). Such an assignment ...

A graph G of order p and size q is edge-magic if there is a bijective function f : V (G) ∪ E(G) −→ {i} i=1 such that f(x) + f(xy) + f(y) = k, for all xy ∈ E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or the weight of f . Furthermore, if f(V (G)) = {i}pi=1 then f is a super edge-magic labeling of G. In this paper we study the valen...

A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

Abstract. For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f defined as f(v) = ∑ f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic grap...

A simple graph 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 H0 P of G isomorphic to H. G is said to be H − supermagic if f(V (G)) = {1, 2, 3, · · · , |V (G)|}. In thi...

An edge-magic total labeling of a graph G is a one-toone map λ from V (G) ∪ E(G) onto the integers {1, 2, · · · , |V (G) ∪ E(G)|} with the property that, there is an integer constant c such that λ(x) + λ(x, y) + λ(y) = c for any (x, y) ∈ E(G). If λ(V (G)) = {1, 2, · · · , |V (G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper we formulate super edge-magic...

An edge-magic total labeling of a graph G is a one-toone map λ from V (G) ∪ E(G) onto the integers {1, 2, · · · , |V (G) ∪ E(G)|} with the property that, there is an integer constant c such that λ(x) + λ(x, y) + λ(y) = c for any (x, y) ∈ E(G). If λ(V (G)) = {1, 2, · · · , |V (G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper, we formulate super edge-magi...

A (p, q)-graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that f(u)+f(v)+f(uv) is a constant for each uv ∈ E(G) and f(V (G)) = {1, 2, . . . , p}. In this paper, we introduce the concept of strong super edgemagic labeling as a particular class of super edge-magic labelings ∗Supported by Slovak VEGA Grant 1/4005/07. †Supported i...