Results 41 to 50 of about 254,578 (267)

On Metric Dimension of Functigraphs

, 2012
The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices.
Bailey R. F., Chartrand G., Chartrand G., Chartrand G., Chen A., CONG X. KANG, Dörfler W., Eroh L., EUNJEONG YI, Garey M. R., Guo J., Harary F., Hernando C., LINDA EROH, Poisson C., Shanmukha B., Slater P. J., Slater P. J.   +17 more
core   +1 more source

Asymptotic Behavior of the Edge Metric Dimension of the Random Graph

Discussiones Mathematicae Graph Theory, 2021
Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
doaj   +1 more source

On Some families of Path-related graphs with their edge metric dimension

Examples and Counterexamples
Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models.
Lianglin Li, Shu Bao, Hassan Raza
doaj   +1 more source

The metric space of geodesic laminations on a surface: I [PDF]

, 2003
We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics.
Casson, Fathi, Francis Bonahon, Gromov, Katok, Minsky, Penner, Xiaodong Zhu   +7 more
core   +4 more sources

Classes of Planar Graphs with Constant Edge Metric Dimension

Complexity, 2021
The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them.
Changcheng Wei, Muhammad Salman, Syed Shahzaib, Masood Ur Rehman, Juanyan Fang   +4 more
doaj   +1 more source

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

Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds

, 2016
Let $V\subset \mathbb{C}\mathbb{P}^n$ be an irreducible complex projective variety of complex dimension $v$ and let $g$ be the K\"ahler metric on $\reg(V)$, the regular part of $V$, induced by the Fubini Study metric of $\mathbb{C}\mathbb{P}^n$.
Bei, Francesco
core   +1 more source

Moduli spaces of toric manifolds [PDF]

, 2013
We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance
A. R. Pires, E Lerman, E Čech, GC Shephard, J Coffey, J-C Hausmann, J-C Hausmann, JJ Duistermaat, JJ Duistermaat, M Atiyah, M Harada, M Kapovich, M Krein, MH Stone, R Lang, S. Sabatini, T Delzant, T. S. Ratiu, V Guillemin, V Guillemin, Vũ Ngọc, Y Karshon, Á Pelayo, Á Pelayo, Á Pelayo, Á Pelayo, Á. Pelayo   +26 more
core   +2 more sources

Hyperprofile-based Computation Offloading for Mobile Edge Networks

, 2017
In recent studies, researchers have developed various computation offloading frameworks for bringing cloud services closer to the user via edge networks.
Calyam, Prasad, Coleman, Kyle, Crutcher, Andrew, Esposito, Flavio, Koch, Caleb, Patman, Jon   +5 more
core   +1 more source

The metric space of geodesic laminations on a surface II: small surfaces [PDF]

, 2005
We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once-punctured torus and the 4-times-punctured sphere.
Bonahon, Francis, Zhu, Xiaodong
core   +2 more sources