The Square of A Directed Graph
J. Kavikumar1, D. Nagarajan2, Yoo Chai Sing3, M. Lathamaheswari4
1J. Kavikumar, Department of Mathematics and Statistics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Malaysia.
2D. Nagarajan, Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India.
3Yoo Chai Sing, Department Third Author Name, Department of Mathematics and Statistics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Malaysia.
4M. Lathamaheswari, Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India.
Manuscript received on November 12, 2019. | Revised Manuscript received on November 23, 2019. | Manuscript published on 30 November, 2019. | PP: 8331-8335 | Volume-8 Issue-4, November 2019. | Retrieval Number: D8993118419/2019©BEIESP | DOI: 10.35940/ijrte.D8993.118419
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Square of Directed Graph, Oriented Graph, Seymour’s Second Neighborhood Conjecture.
Scope of the Article: Graph Algorithms and Graph Drawing.