Results 61 to 70 of about 253,596 (293)

Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete [PDF]

, 2013
We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges.
J. Díaz, P. Bose, R. Tamassia
core   +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

Edge Metric Dimension of Some Classes of Toeplitz Networks

Journal of Mathematics, 2021
Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability.
Dalal Alrowaili, Zohaib Zahid, Muhammad Ahsan, Sohail Zafar, Imran Siddique   +4 more
doaj   +1 more source

On Resolvability Parameters of Some Wheel-Related Graphs

Journal of Chemistry, 2019
Let G=V,E be a simple connected graph, w∈V be a vertex, and e=uv∈E be an edge. The distance between the vertex w and edge e is given by de,w=mindw,u,dw,v, A vertex w distinguishes two edges e1, e2∈E if dw,e1≠dw,e2.
Bin Yang, Muhammad Rafiullah, Hafiz Muhammad Afzal Siddiqui, Sarfraz Ahmad   +3 more
doaj   +1 more source

Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)

Frontiers in Physics, 2020
Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
doaj   +1 more source

On the conformal gauge of a compact metric space [PDF]

, 2012
In this article we study the Ahlfors regular conformal gauge of a compact metric space $(X,d)$, and its conformal dimension $\mathrm{dim}_{AR}(X,d)$. Using a sequence of finite coverings of $(X,d)$, we construct distances in its Ahlfors regular conformal
Piaggio, Matias Carrasco
core   +4 more sources

Mixed metric dimension of graphs with edge disjoint cycles [PDF]

Discrete Applied Mathematics, 2021
In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G)[E(G) is called the mixed metric dimension of G. In this paper we first establish the exact value of the mixed metric dimension of a unicycic graph G which is derived from the structure of G.
Jelena Sedlar, Riste Škrekovski
openaire   +4 more sources

Generalized perimantanes diamondoid structure and their edge-based metric dimensions

AIMS Mathematics, 2022
Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure.
Al-Nashri Al-Hossain Ahmad, Ali Ahmad
doaj   +1 more source

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

A light metric spanner

, 2015
It has long been known that $d$-dimensional Euclidean point sets admit $(1+\epsilon)$-stretch spanners with lightness $W_E = \epsilon^{-O(d)}$, that is total edge weight at most $W_E$ times the weight of the minimum spaning tree of the set [DHN93 ...
Gottlieb, Lee-Ad
core   +1 more source