The convex and weak convex domination number of convex polytopes

Authors

  • Zoran Lj. Maksimović Military Academy, University of Defence, Belgrade, Serbia
  • Aleksandar Lj. Savić Faculty of Mathematics, University of Belgrade, Belgrade, Serbia
  • Milena S. Bogdanović Department of Information Technology, Metropolitan University, Belgrade, Serbia

DOI:

https://doi.org/10.33044/revuma.1739

Abstract

This paper is devoted to solving the weakly convex dominating set problem and the convex dominating set problem for some classes of planar graphs-convex polytopes. We consider all classes of convex polytopes known from the literature and present exact values of weakly convex and convex domination number for all classes, namely $A_n$, $B_n$, $C_n$, $D_n$, $E_n$, $R_n$, $R''_n$, $Q_n$, $S_n$, $S''_n$, $T_n$, $T''_n$ and $U_n$. When $n$ is up to 26, the values are confirmed by using the exact method, while for greater values of $n$ theoretical proofs are given.

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Published

2022-03-22

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