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On Full-separating Sets in Graphs by Chakraborty, Dipayan; Wagler, Annegret K. is a scholarly article available to read on EtoBox.

What is On Full-separating Sets in Graphs about?

Several different types of identification problems have been already studied in the literature, where the objective is to distinguish any two vertices of a graph by their unique neighborhoods in a suitably chosen dominating or total-dominating set of the graph, often referred to as a \emph{code}. To study such problems under a unifying point of view, reformulations of the already studied problems in terms of covering problems in suitably constructed hypergraphs have been provided. Analyzing these hypergraph representations, we introduce a new separation property, called \emph{full-separation}, which has not yet been considered in the literature so far. We study it in combination with both domination and total-domination, and call the resulting codes \emph{full-separating-dominating codes} (or \emph{FD-codes} for short) and \emph{full-separating-total-dominating codes} (or \emph{FTD-codes} for short), respectively. We address the conditions for the existence of FD- and FTD-codes, bounds for their size and their relation to codes of the other types. We show that the problems of determining an FD- or an FTD-code of minimum cardinality in a graph is NP-hard. We also show that the cardi

Author

Chakraborty, Dipayan; Wagler, Annegret K.

Published

2024

Language

EN