Results 51 to 60 of about 8,068,470 (244)

On the Metric Dimension of Cartesian Products of Graphs [PDF]

, 2005
A set S of vertices in a graph G resolves 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 of G.
Brigham R. C., Carlos Seara, Carmen Hernando, Chartrand G., Chartrand G., Currie J., David R. Wood, Erdo˝s P., Goddard W., Goddard W., Greenwell D. L., Harary F., Ignacio M. Pelayo, José Cáceres, Knuth D. E., Lindström B., Lindström B., María L. Puertas, Mercè Mora, Peters‐Fransen J., Poisson C., Saenpholphat V., Shanmukha B., Slater P. J., Slater P. J., Sooryanarayana B., Sooryanarayana B., Yushmanov S. V.   +27 more
core   +5 more sources

Coloring Cantor sets and resolvability of pseudocompact spaces [PDF]

Commentationes Mathematicae Universitatis Carolinae, 2019
Let us denote by $ ( , )$ the statement that $\mathbb{B}( ) = D( )^ $, i.e. the Baire space of weight $ $, has a coloring with $ $ colors such that every homeomorphic copy of the Cantor set $\mathbb{C}$ in $\mathbb{B}( )$ picks up all the $ $ colors. We call a space $X\,$ {\em $ $-regular} if it is Hausdorff and for every non-empty open set $
Juhász, István, Soukup, Lajos, Szentmiklóssy, Zoltán   +2 more
openaire   +3 more sources

New results on metric-locating-dominating sets of graphs [PDF]

, 2016
A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number.
González, Antonio, Hernando Martín, María del Carmen, Mora Giné, Mercè   +2 more
core   +3 more sources

Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure.

PLoS ONE, 2023
The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin, Khurram Shahzad, Abdul Rauf, Fairouz Tchier, Adnan Aslam   +4 more
doaj   +1 more source

On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks

Complex, 2021
In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an
Hua Wang, Muhammad Azeem, M. Nadeem, A. Rehman, A. Aslam   +4 more
semanticscholar   +1 more source

Resolving Sets without Isolated Vertices

Procedia Computer Science, 2015
AbstractLet G be a connected graph. Let W = (w1, w2, ..., wk ) be a subset of V with an order imposed on it. For any v ∈ V, the vector r(v|W) = (d(v, w1), d(v, w2), ..., d(v, wk )) is called the metric representation of v with respect to W. If distinct vertices in V have distinct metric representations, then W is called a resolving set of G.
Chitra, P. Jeya Bala, Arumugam, S.
openaire   +1 more source

Fault-Tolerant Fuzzy Resolving Domination Set [PDF]

International Journal of Applied and Computational Mathematics
R. Shanmugapriya, M. Vasuki, Lenka Čepová, Elangovan Muniyandy, Faruq Mohammad   +4 more
openalex   +2 more sources

Resolving Transition Metal Chemical Space: Feature Selection for Machine Learning and Structure-Property Relationships. [PDF]

Journal of Physical Chemistry A, 2017
Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular ...
J. Janet, Heather J. Kulik
semanticscholar   +1 more source

On Resolving Hop Domination in Graphs

European Journal of Pure and Applied Mathematics, 2021
A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2.
Jerson Mohamad, Helen M. Rara
semanticscholar   +1 more source

On 2-Resolving Sets in the Join and Corona of Graphs

European Journal of Pure and Applied Mathematics, 2021
Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set in 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