Let \(D\) be a simple digraph without loops and parallel arcs. Deng and Kelmans [A. Deng, A. Kelmans, Spectra of digraph transformations, Linear Algebra and its Applications, \(439(2013) 106-132]\) gave the definition of transformation digraphs by introducing symbol \(‘0’\) and \(‘1’\), and investigated the regular and spectra of digraph transformation. In this paper we discuss a class of total transformation digraphs associate with symbol \(‘0’\). Furthermore, we determine the regularity of these ten new kinds of total transformation digraphs and also give necessary and sufficient conditions for them to be strongly connected.
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