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- W4243675815 abstract "The square of an oriented graph is an oriented graph such that if and only if for some , both and exist. According to the square of oriented graph conjecture (SOGC), there exists a vertex such that . It is a special case of a more general Seymour’s second neighborhood conjecture (SSNC) which states for every oriented graph , there exists a vertex such that . In this study, the methods to square a directed graph and verify its correctness were introduced. Moreover, some lemmas were introduced to prove some classes of oriented graph including regular oriented graph, directed cycle graph and directed path graphs are satisfied the SOGC. Besides that, the relationship between SOGC and SSNC are also proved in this study. As a result, the verification of the SOGC in turn implies partial results for SSNC." @default.
- W4243675815 created "2022-05-12" @default.
- W4243675815 date "2019-11-30" @default.
- W4243675815 modified "2023-10-14" @default.
- W4243675815 title "The Square of a Directed Graph" @default.
- W4243675815 doi "https://doi.org/10.35940/ijrte.d8993.118419" @default.
- W4243675815 hasPublicationYear "2019" @default.
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