Enomoto, Llado, Nakamigawa and Ringel (1998) defined the concept of a super (a, 0)-edge-antimagic total labeling and proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In the support of this conjecture, the present paper deals with different results on super (a, d)-edge-antimagic total labeling of subdivided stars for d ∈ {0, 1, 2, 3}.

Let G be a connected graph of order n, minimum degree δ(G), and edge-connectivity κ (G). The graph G ismaximally edge-connected if κ (G) = δ(G) and super edge-connected if every minimum edge-cut consists of edges incident with a vertex of minimum degree. A list (d1, . . . , dn) is graphic if there is a graph with vertices v1, . . . , vn such that d(vi) = di for 1 ≤ i ≤ n. A graphic list D is su...

A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : V ∪E → {i} i=1 such that (1) f(u)+ f(uv)+ f(v) = k ∀uv ∈ E and (2) f(V ) = {i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv ∈ E(G), u′, v′ ∈ V (G) and dG(u, u′) = dG(v, v′) < +∞, then f(u) + f(v) = f(u′) + f(v′). I...

This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.

A (p; q)-graph G is 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)= k is a constant, called the valence of f, for any edge uv of G. Moreover, G is said to be super edge-magic if f(V (G))= {1; 2; : : : ; p}. In this paper, we present some necessary conditions for a graph to be super edge-magic. By means of these, we study the sup...

In this paper, we generalize the concept of super edge-magic graph by introducing the new concept of super edge-magic models.

In this paper we introduce the concept of perfect super edge-magic graphs and we prove some classes of graphs to be perfect super edge-magic.

A graph G is called edge-magic if there exists a bijective function φ : V (G)∪E(G) → {1, 2,. .. , |V (G)|+ |E(G)|} such that φ(x)+φ(xy)+φ(y) is a constant c(φ) for every edge xy ∈ E(G); here c(φ) is called the valence of φ. A graph G is said to be super edge-magic if φ(V (G)) = {1, 2,. .. , |V (G)|}. The super edge-magic deficiency, denoted by μ s (G), is the minimum nonnegative integer n such ...

An edge magic total labeling of a graph G(V,E) with p vertices and q edges is a bijection f from the set of vertices and edges to such that for every edge uv in E, f(u) + f(uv) + f(v) is a constant k. If there exist two constants k1 and k2 such that the above sum is either k1 or k2, it is said to be an edge bimagic total labeling. A total edge magic (edge bimagic) graph is called a super edge m...