Generalized $k$-Rainbow and Generalized 2-Rainbow Domination in Graphs

Document Type : Research Article

Authors

1 Department of Mathematics and Computer Sciences, Faculty of Sciences University of Qom, Qom, Iran

2 Department of Mathematics, Farahan Branch, Islamic Azad University Farahan, Iran.

3 Department of Mathematics, Faculty of Sciences, University of Qom, Qom, Iran

Abstract

Assume we have a set of $k$ colors and to each vertex of a graph $G$ we assign an arbitray of these colors‎. ‎If we require that each vertex to set is assigned has in its closed neighborhood all $k$ colors‎, ‎then this is called the generalized $k$-rainbow dominating function of a graph $G$‎. ‎The corresponding $\gamma_{gkr}$‎, ‎which is the minimum sum of numbers of assigned colors over all vertices of $G$‎, ‎is called the g$k$-rainbow domination number of $G$‎. ‎In this paper‎, ‎we present a linear algorithms for determining a minimum generalized $2$-rainbow dominating set of a tree and on $GP(n,2)$.

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References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 8, Issue 1
July 2023
Pages 26-30

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History

  • Receive Date: 13 December 2023
  • Revise Date: 05 February 2024
  • Accept Date: 24 February 2024
  • Publish Date: 28 February 2024

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