We bring into attention the interplay between model theory of committed graphs (1-regular graphs) and their palindromic characteristic in the domain of formal languages. We prove some model theoretic properties of committed graphs and then give a characterization of them in the formal language domain using palindromes. We show in the first part of the paper that the theory of committed graphs and the theory of infinite committed graphs differ in terms of completeness. We give the observation that theories of finite and infinite committed graphs are both decidable. The former is finitely axiomatizable, whereas the latter is not. We note that every committed graph is isomorphic to the structure of integers. In the second part, as our main focus of the paper and using some of the results in the first section, we give a characterization of committed graphs based on the notion of finite and infinite palindrome strings.

中文翻译：

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提交图的回文特征及一些模型理论性质

我们关注承诺图（1-正则图）的模型理论与其在形式语言领域的回文特征之间的相互作用。我们证明了提交图的一些模型理论性质，然后使用回文在形式语言域中给出了它们的特征。我们在论文的第一部分表明，承诺图理论和无限承诺图理论在完整性方面有所不同。我们观察到有限和无限承诺图的理论都是可判定的。前者是有限公理化的，而后者不是。我们注意到每个提交的图都与整数结构同构。在第二部分中，作为本文的主要重点并使用第一部分的一些结果，