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Disjoint dominating and 2-dominating sets in graphs

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arxiv 1903.06129 v1 pith:4CPLGSCB submitted 2019-03-14 math.CO

Mateusz Miotk , Jerzy Topp , Pawe{l} Żyliński This is my paper · ORCID
classification math.CO
keywords dominatingdisjointgraphgraphssetscharacterizationsconcerninghardness
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abstract

A graph $G$ is a $D\!D_2$-graph if it has a pair $(D,D_2)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_2$ is a 2-dominating set of $G$. We provide several characterizations and hardness results concerning $D\!D_2$-graphs.

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  1. Minimal graphs with disjoint dominating and paired-dominating sets

    math.CO 2019-08 conditional novelty 7.0 of 10

    A connected graph with no redundant edges that still admits a dominating set disjoint from a paired-dominating set is exactly a 2-subdivision graph of a connected graph free of isolated vertices and good subgraphs, ex...

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