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Communication Dans Un Congrès Année : 2024

Open-Separating Dominating Codes in Graphs

Résumé

Using dominating sets to separate vertices of graphs is a well-studied problem in the larger domain of identification problems. In such problems, the objective is to choose a suitable dominating set $C$ of a graph $G$ such that the neighbourhoods of all vertices of $G$ have distinct intersections with $C$. Such a dominating and separating set $C$ is often referred to as a \emph{code} in the literature. Depending on the types of dominating and separating sets used, various problems arise under various names in the literature. In this paper, we introduce a new problem in the same realm of identification problems whereby the code, called \emph{open-separating dominating code}, or \emph{OSD-code} for short, is a dominating set and uses open neighbourhoods for separating vertices. The paper studies the fundamental properties concerning the existence, hardness and minimality of OSD-codes. Due to the emergence of a close and yet difficult to establish relation of the OSD-codes with another well-studied code in the literature called open locating dominating codes, or OLD-codes for short, we compare the two on various graph families. Finally, we also provide an equivalent reformulation of the problem of finding OSD-codes of a graph as a covering problem in a suitable hypergraph and discuss the polyhedra associated with OSD-codes, again in relation to OLD-codes of some graph families already studied in this context.
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Dates et versions

hal-04615473 , version 1 (18-06-2024)

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Dipayan Chakraborty, Annegret Wagler. Open-Separating Dominating Codes in Graphs. International Symposium on Combinatorial Optimization, May 2024, Tenerife (Canary Islands), Spain. pp.137-151, ⟨10.1007/978-3-031-60924-4_11⟩. ⟨hal-04615473⟩
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