Abstract
Design and analysis of interconnection networks has been a major topic in recent years due to its recent advances in parallel and distributed system. Although the remarkable Cayley graphs have played a prominent role in interconnection networks, there has been an increasing interest in studying non-Cayley graphs. In this paper, we present characterization theorems on certain classes of non-Cayley graphs. To attain the characterization, we approach the slope number and domatic number for investigation and studied elaborately for non-Cayley graphs such as generalized Petersen graph, butterfly and Benes network. Here, the slope number is about minimizing the slopes, and domatic number is about partitioning the vertices into dominating sets. The important goal of the paper is to yield a relationship between slope number and domatic number based on the characterization that satisfies equality condition.
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References
Antony Mary A, Amutha A (2018) Domatic number of a Butterfly network. Int J Pure Appl Mathe 119(11):303–311
Antony Mary A, Amutha A (2019) The performance on slope number of hypercube, normal representation of butterfly and Benes networks. Int J Eng Adv Technol 9(1):2349–2352
Berge C (1973) Graphs and hypergraphs. North Holland, Amsterdam
Cockayne EJ, Hedetnieme ST (1977) Towards a theory of domination in graphs. Networks 7
Kaplan H, Shamir R (1994) The domatic number problem on some perfect graph families. Inf Process Lett 49:51–56
Manuel P, Abd-El-Bar MI, Rajasingh I, Rajan B (2008) An efficient representation of Benes network and its applications. J Discrete Algorithms 6:11–19
Ore O (1962) Theory of graphs. Amer Maths Soc Collaq Pub 38
Wade GA, Chu JH (1994) Drawability of complete graphs using a minimal slope set. Comput J 37(2):139–142
Xu J (2001) Topological structures and analysis of interconnection network. Kluwer Academic Publishers
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Antony Mary, A., Amutha, A. (2022). A Study on Slope Number and Domatic Number on Certain Classes of Non-Cayley Graphs. In: Srivastava, P., Thivagar, M.L., Oros, G.I., Tan, C.C. (eds) Mathematical and Computational Intelligence to Socio-scientific Analytics and Applications. Lecture Notes in Networks and Systems, vol 518. Springer, Singapore. https://doi.org/10.1007/978-981-19-5181-7_25
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DOI: https://doi.org/10.1007/978-981-19-5181-7_25
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