Domination number of middle graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, School of Sciences, Ilam University, P.O.Box 69315-516, Ilam, Iran.

2 Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan.

3 Hokkaido University, Department of Mathematics

Abstract

In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the domination number of some families of graphs such as star graphs, double start graphs, path graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs and friendship graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the domination number of middle graphs.

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References

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History

  • Receive Date: 23 October 2021
  • Revise Date: 24 May 2022
  • Accept Date: 28 May 2022
  • Published Online: 01 June 2023

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