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- W3099682263 abstract "Cycle rank is an important notion that is widely used to classify, understand, and discover new chemical compounds. We propose a method to enumerate all non-isomorphic tree-like graphs of a given cycle rank with self-loops and no multiple edges. To achieve this, we develop an algorithm to enumerate all non-isomorphic rooted graphs with the required constraints. The idea of our method is to define a canonical representation of rooted graphs and enumerate all non-isomorphic graphs by generating the canonical representation of rooted graphs. An important feature of our method is that for an integer n≥1, it generates all required graphs with n vertices in O(n) time per graph and O(n) space in total, without generating invalid intermediate structures. We performed some experiments to enumerate graphs with a given cycle rank from which it is evident that our method is efficient. As an application of our method, we can generate tree-like polymer topologies of a given cycle rank with self-loops and no multiple edges." @default.
- W3099682263 created "2020-11-23" @default.
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- W3099682263 date "2020-11-13" @default.
- W3099682263 modified "2023-09-25" @default.
- W3099682263 title "Enumerating Tree-Like Graphs and Polymer Topologies with a Given Cycle Rank" @default.
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- W3099682263 doi "https://doi.org/10.3390/e22111295" @default.
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