Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic graph then q ≤ 2p− 3. Furthermore, if G is super edge-magic and q = 2p− 3, then the girth of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then q ≤ 2p − 5. In this paper we show that there are infinitely many graphs which are super edge-magic, have girth 5, and q =...

Let G1, G2, ..., Gn be a family of disjoint stars. The tree obtained by joining a new vertex a to one pendant vertex of each star Gi is called a banana tree. In this paper we determine the super edge-magic total labelings of the banana trees that have not been covered by the previous results [15].

A (p,q) graph G is called super edge-magic if there exists a bijective function f from V (G) ∪ E(G) to {1, 2,. .. , p + q} such that f (x) + f (xy) + f (y) is a constant k for every edge xy of G and f (V (G)) = {1, 2,. .. , p}. Furthermore, the super edge-magic deficiency of a graph G is either the minimum nonnegative integer n such that G ∪ nK 1 is super edge-magic or +∞ if there exists no suc...

A (p, q) graph G is called 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 constant for any edge uv of G. Moreover, G is said to be super edgemagic if f(V (G)) = {1, 2, . . . , p}. Every super edge-magic (p, q) graph is harmonious, sequential and felicitous whenever it is a tree or satisfies q ≥ p. In this paper, we prove...

Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...

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 (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...