In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these graphs can or cannot occur as the prime character degree graph of a solvable group. An obvious expansion and generalization can also be considered, of which we make mention.

中文翻译：

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在图族中出现的素数度图

在本文中，我们研究了在其补中不包含奇数圈的连通图族。具体来说，我们考虑由以特定方式连接的两个完整图形成的图。我们确定这些图中的哪些可以或不能作为可解群的主要特征度图出现。也可以考虑一个明显的扩展和概括，我们提到了这一点。