Matches in SemOpenAlex for { <https://semopenalex.org/work/W4309968459> ?p ?o ?g. }
Showing items 1 to 56 of
56
with 100 items per page.
- W4309968459 abstract "A locating-dominating set in an undirected graph is a subset of vertices $S$ such that $S$ is dominating and for every $u,v notin S$, we have $N(u)cap Sne N(v)cap S$. In this paper, we consider the oriented version of the problem. A locating-dominating set in an oriented graph is a set $S$ such that for every $win V$, $N[w]^-cap S=emptyset$ and for each pair of vertices $u,vin Vsetminus S$, $N^-(u)cap Sne N^-(v)cap S$. We consider the following two parameters. Given an undirected graph $G$, we look for $overset{rightarrow}{gamma}_{LD}(G)$ ($overset{rightarrow}{Gamma}_{LD}(G))$ which is the size of the smallest (largest) optimal locating-dominating set over all orientations of $G$. In particular, if $D$ is an orientation of $G$, then $overset{rightarrow}{gamma}_{LD}(G)leq{gamma}_{LD}(D)leqoverset{rightarrow}{Gamma}_{LD}(G)$. For the best orientation, we prove that, for every twin-free graph $G$ on $n$ vertices, $overset{rightarrow}{gamma}_{LD}(G)le n/2$ proving a ``directed version'' of a conjecture on $gamma_{LD}(G)$. Moreover, we give some bounds for $overset{rightarrow}{gamma}_{LD}(G)$ on many graph classes and drastically improve the value $n/2$ for (almost) $d$-regular graphs by showing that $overset{rightarrow}{gamma}_{LD}(G)in O(log d/dcdot n)$ using a probabilistic argument. While $overset{rightarrow}{gamma}_{LD}(G)leqgamma_{LD}(G)$ holds for every graph $G$, we give some graph classes graphs for which $overset{rightarrow}{Gamma}_{LD}(G)geq{gamma}_{LD}(G)$ and some for which $overset{rightarrow}{Gamma}_{LD}(G)leq {gamma}_{LD}(G)$. We also give general bounds for $overset{rightarrow}{Gamma}_{LD}(G)$. Finally, we show that for many graph classes $overset{rightarrow}{Gamma}_{LD}(G)$ is polynomial on $n$ but we leave open the question whether there exist graphs with $overset{rightarrow}{Gamma}_{LD}(G)in O(log n)$." @default.
- W4309968459 created "2022-11-30" @default.
- W4309968459 creator A5016880662 @default.
- W4309968459 creator A5044190443 @default.
- W4309968459 creator A5071276295 @default.
- W4309968459 creator A5087008157 @default.
- W4309968459 date "2021-12-03" @default.
- W4309968459 modified "2023-10-18" @default.
- W4309968459 title "Locating-dominating sets: from graphs to oriented graphs" @default.
- W4309968459 doi "https://doi.org/10.48550/arxiv.2112.01910" @default.
- W4309968459 hasPublicationYear "2021" @default.
- W4309968459 type Work @default.
- W4309968459 citedByCount "0" @default.
- W4309968459 crossrefType "posted-content" @default.
- W4309968459 hasAuthorship W4309968459A5016880662 @default.
- W4309968459 hasAuthorship W4309968459A5044190443 @default.
- W4309968459 hasAuthorship W4309968459A5071276295 @default.
- W4309968459 hasAuthorship W4309968459A5087008157 @default.
- W4309968459 hasBestOaLocation W43099684591 @default.
- W4309968459 hasConcept C114614502 @default.
- W4309968459 hasConcept C118615104 @default.
- W4309968459 hasConcept C132525143 @default.
- W4309968459 hasConcept C146661039 @default.
- W4309968459 hasConcept C16345878 @default.
- W4309968459 hasConcept C2524010 @default.
- W4309968459 hasConcept C2780990831 @default.
- W4309968459 hasConcept C3018234147 @default.
- W4309968459 hasConcept C33923547 @default.
- W4309968459 hasConcept C80899671 @default.
- W4309968459 hasConceptScore W4309968459C114614502 @default.
- W4309968459 hasConceptScore W4309968459C118615104 @default.
- W4309968459 hasConceptScore W4309968459C132525143 @default.
- W4309968459 hasConceptScore W4309968459C146661039 @default.
- W4309968459 hasConceptScore W4309968459C16345878 @default.
- W4309968459 hasConceptScore W4309968459C2524010 @default.
- W4309968459 hasConceptScore W4309968459C2780990831 @default.
- W4309968459 hasConceptScore W4309968459C3018234147 @default.
- W4309968459 hasConceptScore W4309968459C33923547 @default.
- W4309968459 hasConceptScore W4309968459C80899671 @default.
- W4309968459 hasLocation W43099684591 @default.
- W4309968459 hasLocation W43099684592 @default.
- W4309968459 hasOpenAccess W4309968459 @default.
- W4309968459 hasPrimaryLocation W43099684591 @default.
- W4309968459 hasRelatedWork W1999589324 @default.
- W4309968459 hasRelatedWork W2010333092 @default.
- W4309968459 hasRelatedWork W2090515205 @default.
- W4309968459 hasRelatedWork W2619045485 @default.
- W4309968459 hasRelatedWork W2982829914 @default.
- W4309968459 hasRelatedWork W3201982285 @default.
- W4309968459 hasRelatedWork W4290190164 @default.
- W4309968459 hasRelatedWork W4300410646 @default.
- W4309968459 hasRelatedWork W4309968459 @default.
- W4309968459 hasRelatedWork W4362737182 @default.
- W4309968459 isParatext "false" @default.
- W4309968459 isRetracted "false" @default.
- W4309968459 workType "article" @default.