Extension of α-labelings of quadratic graphs

α Valuations of Special Classes of Quadratic Graphs

An Integer Programming Model and a Tabu Search Algorithm to Generate α-labeling of Special Classes of Quadratic Graphs

First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...

Constructions of antimagic labelings for some families of regular graphs

In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

A new application of the ⊗h-product to α-labelings

The weak tensor product was introduced by Snevily as a way to construct new graphs that admit α-labelings from a pair of known α-graphs. In this article, we show that this product and the application to α-labelings can be generalized by considering as a second factor of the product, a family Γ of bipartite (p, q)-graphs, p and q fixed. The only additional restriction that we should consider is ...