On the uniqueness of the factorization of power digraphs modulo
Amplify Sawkmie
North-Eastern Hill University, Shillong, Meghalaya, IndiaMadan Mohan Singh
North-Eastern Hill University, Shillong, Meghalaya, India
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Abstract
For each pair of integers and , a digraph is one with vertex set and for which there exists a directed edge from to if . Using the Chinese Remainder Theorem, the digraph can be written as a direct product of digraphs for all such that . A fundamental constituent , where , is a subdigraph of induced on the set of vertices which are multiples of and are relatively prime to all primes . In this paper, we investigate the uniqueness of the factorization of trees attached to cycle vertices of the type , , and , and in general, the uniqueness of . Moreover, we provide a necessary and sufficient condition for the isomorphism of the fundamental constituents and of and respectively for .
Cite this article
Amplify Sawkmie, Madan Mohan Singh, On the uniqueness of the factorization of power digraphs modulo . Rend. Sem. Mat. Univ. Padova 140 (2018), pp. 185–219
DOI 10.4171/RSMUP/8