Abstract
Let \(D=(V,E)\) be a digraph and \(u ,v\in V(D)\). The metric, maximum distance is defined by \(md(u,v)=\max \{\overrightarrow{d}(u,v), \overrightarrow{d}(v,u)\}\) where \(\overrightarrow{d}(u,v)\) denote the length of a shortest directed \(u-v\) path in D. The relationship between the boundary-type sets of the lexicographic product of two digraphs and its factor graphs have been studied in this article.
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Acknowledgements
Prasanth G. Narasimha-Shenoi and Mary Shalet Thottungal Joseph are supported by Science and Engineering Research Board, a statutory body of Government of India under their Extra Mural Research Funding No. EMR/2015/002183. Also, their research was partially supported by Kerala State Council for Science Technology and Environment of Government of Kerala under their SARD project grant Council(P) No. 436/2014/KSCSTE. Prasanth G. Narasimha-Shenoi is also supported by Science and Engineering Research Board, under their MATRICS Scheme No. MTR/2018/000012.
The authors thank the anonymous referees for their valuable comments which helped in improving the article.
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Changat, M., Narasimha-Shenoi, P.G., Joseph, M.S.T. (2021). Lexicographic Product of Digraphs and Related Boundary-Type Sets. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_18
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