Super Domination: Graph Classes, Products and Enumeration
Nima Ghanbari, Gerold J\"ager, Tuomo Lehtil\"a

TL;DR
This paper studies the super dominating set problem, a variant of the dominating set problem, providing bounds, exact counts for specific graph classes, and exploring properties of super dominating sets in cycles.
Contribution
It introduces tight bounds for super domination numbers in various graph operations and characterizes the number of minimum super dominating sets in certain graph classes.
Findings
Bounds for super domination number in graph products and sums
Exact counts of super dominating sets in specific graph classes
Surprising variation in the number of super dominating sets in cycles
Abstract
The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph , a dominating set of is a subset such that every vertex in is adjacent to at least one vertex in . Furthermore, the DSP is the problem of finding a minimum-size dominating set and the corresponding minimum size, the domination number of . In this, work we investigate a variant of the DSP, the super dominating set problem (SDSP), which has attracted much attention during the last years. A dominating set is called a super dominating set of , if for every vertex , there exists a such that . Analogously, the SDSP is to find a minimum-size super dominating set, and the corresponding minimum size, the super…
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Taxonomy
TopicsAdvanced Graph Theory Research
