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- W4300983767 abstract "In a graph $G$, a set $Dsubseteq V(G)$ is called 2-dominating set if each vertex not in $D$ has at least two neighbors in $D$. The 2-domination number $gamma_2(G)$ is the minimum cardinality of such a set $D$. We give a method for the construction of 2-dominating sets, which also yields upper bounds on the 2-domination number in terms of the number of vertices, if the minimum degree $delta(G)$ is fixed. These improve the best earlier bounds for any $6 le delta(G) le 21$. In particular, we prove that $gamma_2(G)$ is strictly smaller than $n/2$, if $delta(G) ge 6$. Our proof technique uses a weight-assignment to the vertices where the weights are changed during the procedure." @default.
- W4300983767 created "2022-10-04" @default.
- W4300983767 creator A5064454231 @default.
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- W4300983767 date "2016-12-25" @default.
- W4300983767 modified "2023-10-16" @default.
- W4300983767 title "Bounds on the 2-domination number" @default.
- W4300983767 doi "https://doi.org/10.48550/arxiv.1612.08301" @default.
- W4300983767 hasPublicationYear "2016" @default.
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