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Published
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The convex and weak convex domination number of convex polytopes
Volume 63, no. 1
(2022),
pp. 51–68
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 by the Unión Matemática Argentina |
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