Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 1 2021 05 01 Classification of problems of determining the maximum common fragments for two structures of a temporal digraph 869 875 4942 10.22075/ijnaa.2021.4942 EN Ali Rashid Ibrahim Department of Applied Mathematics, College of Science, University of Anbar, Ramadi, Iraq Journal Article 2020 11 26 A new approach is proposed for classifying the problems of determining the maximum common fragments $(M C F)$ for two connected structures included in the $T$-digraph, based on the type of the maximum common fragment. A tree of classification the problems of determining the maximum common fragments $(M C F)$ for two structures $t_{i} G, t_{j} G\left(M C F\left(t_{i} G, t_{j} G\right)\right)$ included in the $T$-digraph is proposed. Examples are given for a digraph $t G$ with three types of its fragments (parts), and for five connectivity types of digraphs. The formulation of six basic problems of determining the maximum common fragments $ (MCF) $ for two connected structures included in the $T$-digraph is given. A classification is proposed for an isomorphic embedding of a digraph into another. https://ijnaa.semnan.ac.ir/article_4942_59522f789923050dbd9f007f0f3a3ceb.pdf