A sequence of vertices in a graph G without isolated vertices is called a total dominating sequence if every vertex v in the sequence has a neighbor which is adjacent to no vertex preceding v in the sequence, and at the end every vertex of G has at least one neighbor in the sequence. Minimum and maximum lengths of a total dominating sequence is the total domination number of G (denoted by ${\gamma }_t(G)$) and the Grundy total domination number of G (denoted by ${\gamma }_{gr}^t(G)$), respectively. In this paper, we study graphs where all total dominating sequences have the same length. For every positive integer k, we call G a total k-uniform graph if every total dominating sequence of G is of length k, that is, ${\gamma }_t(G)={\gamma }_{gr}^t(G)=k$. We prove that there is no total k-uniform graph when k is odd. In addition, we present a total 4-uniform graph which stands as a counterexample for a conjecture by [11] and provide a connected total 8-uniform graph. Moreover, we prove that every total k-uniform, connected and false twin-free graph is regular for every even k. We also show that there is no total k-uniform chordal connected graph with $k\ge 4$ and characterize all total k-uniform chordal graphs.

如果图G 中没有孤立顶点的顶点序列称为全支配序列，如果该序列中的每个顶点v都有一个邻居，该邻居与序列中v之前的没有顶点相邻，并且最后G 的每个顶点至少有序列中的一个邻居。总支配序列的最小和最大长度是G的总支配数（表示为${\gamma }_{吨}(G)$) 和G的 Grundy 总支配数（表示为${\gamma }_{Gr}^{吨}(G)$）， 分别。在本文中，我们研究了所有总支配序列都具有相同长度的图。对于每一个正整数ķ，我们称之为ģ共ķ -uniform图表如果每一个全控制序列ģ是长度ķ，即，${\gamma }_{吨}(G)={\gamma }_{Gr}^{吨}(G)=克$. 我们证明了当k为奇数时，不存在全k一致图。此外，我们提出了一个总共 4-uniform 图，它作为 [11] 猜想的反例，并提供了一个连接的全 8-uniform 图。此外，我们证明了对于每个偶数k，每个总k一致、连通和假双胞胎图都是正则的。我们还表明，不存在总k -uniform chordal connected graph with$克\ge 4$并刻画所有总k一致弦图。