The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph over LA-group and GCLAP-graph. Further, we investigate a few properties of them to show that each simple graph of order three, four, and five (except cycle graph of order five which may or may not be a GCLAP-graph) is a GCLAP-graph and then we prove this result.

中文翻译：

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La-group和La-Polygroup上的Cayley图

本文的目的是研究简单图，这些简单图是LA-polygroup上的广义Cayley图。在这方面，我们为构建LA-polygroups构建了两个新的扩展。然后，我们定义了LA-group和GCLAP-graph上的Cayley图。此外，我们研究了它们的一些属性，以表明三阶，四阶和五阶的每个简单图（五阶循环图可能不是GCLAP图）都为GCLAP图，然后证明这个结果。