In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity. Moreover, this code can achieve zero-error capacity when the symbols in a vertex with degree one are the same. We further apply our method to the one-edge graphs representing the binary channels with two memories. There are 28 possible graphs, which can be organized into 11 categories based on their symmetries. The code constructed by our method is proved to achieve the zero-error capacity for all these graphs except for the two graphs in Case 11.

翻译：本文研究了由图表征的带记忆信道的零差错容量问题。针对任意含单条边的图结构，我们提出了一种编码构造方法，从而确定了其零差错容量的下界。特别地，当度数为1的顶点包含相同符号时，该编码方案能够达到零差错容量。我们将该方法进一步应用于表征双记忆二进制信道的单边图，共存在28种可能的图结构，根据对称性可归纳为11个类别。研究证明，除第11类中的两个特例外，本文提出的编码方法对其余所有图均能达到零差错容量。