A labeling of a graph is a bijective function onto its edges from the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for every pair of distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph ot...

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomp...

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}.

A handicap distance antimagic labeling of a graph G = (V,E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(xi) = i and the sequence of the weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑ xj∈N(xi) f(xj)) forms an increasing arithmetic progression with difference one. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagi...

An antimagic labeling of a directed graph D with n vertices and m arcs is a bijection from the set of arcs of D to the integers {1, . . . ,m} such that all n oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. An undirected graph G is said to have an antimagic orientation i...

In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which ha...

In this paper we introduce two new labelings called product antimagic labeling and total product antimagic labeling for directed graphs and show the existence of the same for Cayley digraphs of 2-generated 2groups. AMS Mathematics Subject Classification : 05C78.

An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. ...

An antimagic labeling of an undirected graph G with n vertices and m edges is a bijection from the set of edges of G to the integers {1, . . . ,m} such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. A graph is called antimagic if it admits an antimagic labeling. In [6], Hartsfield and Ringel conjectured that every si...

An antimagic labeling of a finite undirected simple graph with m edges and n vertices is a bijection from the set of edges to the integers 1, . . . , m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that e...