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.

Let \(G=(V, E)\) be a simple graph and \(H\) subgraph of \(G\). Then \(G\) admits an \(H\)-covering, if every edge in \(E(G)\) belongs to at least one that is isomorphic \(H\). An \((a,d)-H\)-antimagic total labeling bijection \(f:V(G)\cup E(G)\rightarrow \{1, 2, 3,\dots, |V(G)| + |E(G)|\}\) such for all subgraphs \(H'\) \(H\), the weights \(w(H') =\sum_{v\in V(H')} f (v) \sum_{e\in E(H')} (e)\...

A group distance magic labeling or aG-distance magic labeling of a graph G = (V, E) with |V | = n is a bijection f from V to an Abelian group G of order n such that the weight w(x) = ∑y∈NG (x) f (y) of every vertex x ∈ V is equal to the same element μ ∈ G, called the magic constant. In this paper we will show that if G is a graph of order n = 2p(2k + 1) for some natural numbers p, k such that d...

Various graph labelings that generalize the idea of a magic square have been discussed. In particular a magic labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, ... , v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. Prope...

A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H...

Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful la...

In this paper we prove that the extended triplicate graph (ETG) of finite paths admits product E-cordial, total product E-cordial labelings. We show that ETG of finite paths of length n where n ∉ {4m-3|m∈N} admits E-Cordial, total E-cordial labelings and also we prove the existence of Z3 – magic labeling for the modified Extended Triplicate graph.

For a graph G = (V, E), a bijection f from V(G) ∪ E(G) → {1, 2, . . . , |V(G)| + |E(G)|} is called (a, d)-edge-antimagic total ((a, d)EAT) labeling of G if the edge-weights w(xy) = f(x) + f(y) + f(xy), xy ∈ E(G), form an arithmetic progression starting from a and having a common difference d, where a > 0 and d ≥ 0 are two fixed integers. An (a, d)-EAT labeling is called super (a, d)-EAT labelin...