SUPER MAGIC AND ANTIMAGIC LABELINGS OF DISJOINT UNION OF PLANE GRAPHS Ali Ahmad, Martin Bača, Marcela Lascsáková, Andrea Semaničová-Feňovčíková 2,3 College of computer and information system, Jazan University, Jazan, Saudi Arabia Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovak Republic Abdus Salam School of Mathematical Sciences, G. C. University, Lahore, P...

A connected graph G is said to be (a, d)-antimagic, for some positive integers a and d, if its edges admit a labeling by the integers 1,2, ... , IE( G) I such that the induced vertex labels consist of an arithmetic progression with the first term a and the common difference d. In this paper we prove that the generalized Petersen graph P(n,2) is (3n2+6, 3)-antimagic for n == 0 (mod 4), n ~ B.

The concept of antimagic labelings a graph is to produce distinct vertex sums by labeling edges through consecutive numbers starting from one. A long-standing conjecture that every connected graph, except single edge, antimagic. Some graphs are known be antimagic, but little has been about sparse graphs, not even trees. This paper studies weak version called k-shifted-antimagic which allow the ...

Let G = (V,E) be a (p, q)-graph of order p and size q and f be a bijection from the set V ∪ E to the set of the first p + q natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say f is an (a, d)-vertex-antimagic total labeling if the vertex-weights form an arithmetic progression with the initial term a and the common difference d. Such a labe...

In 1980, Enomoto et al. proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In this paper, we give a partial support for the correctness of this conjecture by formulating some super (a, d)edge-antimagic total labelings on a subclass of subdivided stars denoted by T (n, n + 1, 2n + 1, 4n + 2, n5, n6, . . . , nr) for different values of the edgeantimagic labeling...

A (p, q)-graph G is (a, d)-edge antimagic total if there exists a bijection f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2, . . . , p} and the edge labels are {p+ 1, p+ 2, . . . ,...

Let $A$ be a nontrivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to \setminus \{0\}$ such that the induced vertex $f^+: V(G) A$, defined by $f^+(v) \Sigma$ $\{f(u,v): (u, v) \in \}$, one-to-one map. In this paper, we analyze group-antimagic property for Cartesian products, hexagonal nets and theta graphs.

Tree is one of the most studied and practically useful classes of graphs and is the attention of a great number of studies. There is absence of generalized results for tree as a class and even for one kind of labeling as whole. Only specialized results exist limited to specific types of trees only. A number of conjectures stand being unsolved. Graham and Sloane (1980) conjectured trees to be Ha...