On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
doaj +1 more source
On the Minimum Differentially Resolving Set Problem for Diffusion Source Inference in Networks
AAAI Conference on Artificial Intelligence, 2016 In this paper we theoretically study the minimum Differentially Resolving Set (DRS) problem derived from the classical sensor placement optimization problem in network source locating.
Chuan Zhou +5 more
semanticscholar +1 more source
Non-Isolated Resolving Sets of Corona Graphs with Some Regular Graphs
Mathematics, 2022 Let G be a connected, simple, and finite graph. For an ordered set W={w1,w2,…,wk}⊆V(G) and a vertex v of G, the representation of v with respect to W is the k-vector r(v|W)=(dG(v,w1),…,dG(v,wk)).
W. Abidin, A. Salman, S. Saputro
semanticscholar +1 more source
Resolving sets tolerant to failures in three-dimensional grids [PDF]
Mediterranean Journal of Mathematics, 2021 An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set.
M. Mora +2 more
semanticscholar +1 more source
Application of Metric Dimensions to Minimize the Installation of Fire Sensors on The Rectorate Building of Pasifik Morotai University [PDF]
MATEC Web of Conferences, 2022 The metric dimension of the connected graph G for each 𝑣 𝜖 𝑉(𝐺) to the set W is . The set r (ν|W) = (d(ν, w1), d(ν,w2),…d(ν,wk) W is called the resolving set if every vertex u,v in G, if u ≠ ν , then r (u|W) ≠ r (ν|W) .
Parera Cicilya Orissa F. +3 more
doaj +1 more source
Restrained 2-Resolving Sets in the Join, Corona and Lexicographic Product of Two Graphs
European Journal of Pure and Applied Mathematics, 2022 Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions.
Jean Mansanadez Cabaro, Helen M. Rara
semanticscholar +1 more source
Resolvent Estimates for Normally Hyperbolic Trapped Sets [PDF]
Annales Henri Poincaré, 2011 Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic.
Wunsch, Jared, Zworski, Maciej
openaire +2 more sources
Limit sets of stable Cellular Automata [PDF]
, 2013 We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism.
Alexis Ballier, Santiago Chile
core +1 more source
DETERMINING THE DOMINANT METRIC DIMENSION FOR VARIOUS GRAPHS [PDF]
Journal of Mechanics of Continua and Mathematical SciencesIn this paper, we examine the dominating metric dimension of various graph types. A resolving set is a subset of vertices that uniquely identifies each vertex in the graph based on its distances to others, and the metric dimension is the minimum size of
Iqbal M. Batiha +2 more
doaj +1 more source
Resolving Independent Dominating Set pada Graf Bunga, Graf Gear, dan Graf Bunga Matahari
Contemporary Mathematics and Applications (ConMathA), 2023 Resolving independent dominating set is the development of metric dimension and independent dominating set. Resolving independent dominating sets is a concept which discusses about determining the minimum vertex on a graph provided that the vertex that ...
Rafiantika Megahniah Prihandini +4 more
doaj +1 more source