Graph labellings have been a very fruitful area of research in the last fourdecades. However, despite the staggering number of papers published in thefield (over 1000), few general results are available, and most papers deal withparticular classes of graphs and methods. Here we approach the problem from thecomputational viewpoint, and in a quite general way. We present the existenceproblem of a particular labelling as a combinatorial optimization problem, thenwe discuss the possible strategies to solve it, and finally we present aheuristic for finding different classes of labellings, like vertex-, edge-, orface-magic, and $(a, d)$-antimagic $(v, e, f)$-labellings. The algorithm hasbeen implemented in C++ and MATLAB, and with its aid we have been able toderive new results for some classes of graphs, in particular, vertex-antimagicedge labellings for small graphs of the type $P_2^r \times P_3^s$, for which nogeneral construction is known so far.
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机译：在过去的四个十年中，图形标签一直是非常富有成果的研究领域。但是，尽管该领域发表的论文数量惊人（超过1000），但可获得的一般结果很少，并且大多数论文都涉及特定类别的图和方法。在这里，我们从计算的角度，以一种相当普遍的方式来解决这个问题。我们将特定标签的存在问题作为组合优化问题提出，然后我们讨论解决该问题的可能策略，最后我们提出启发式算法来查找不同类别的标签，例如顶点，边线，面魔术和$（a ，d）$-反磁性$（v，e，f）$-标签。该算法已在C ++和MATLAB中实现，借助它，我们能够推导出某些类图的新结果，尤其是对于类型为$ P_2 ^ r \ times P_3 ^ s $的小图的顶点-抗磁标记，到目前为止，它的一般构造是已知的。
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