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 𝑄(𝑚, 4𝑘). 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 𝑄(𝑚, 4𝑘), 6 ≤ 𝑚 ≤ 10, 2 ≤ 𝑘 ≤ 10, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory can be modeled and solved by an integer programming model and a metaheuristic approach.