IEEE/ACM Transactions on Networking, ISSN 1063-6692, 12/2016, Volume 24, Issue 6, pp. 3620 - 3633

Energy efficiency is an important issue in the study of wireless sensor networks. Given a set of targets and a set of sensors with bounded lifetime, the...

Greedy algorithms | Wireless sensor networks | Strips | uniform sensing range | multi-cover | Approximation algorithms | maximum lifetime | weight | Sensors | Partitioning algorithms | Approximation algorithm | IEEE transactions | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHMS | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TARGET COVERAGE | CONNECTED DOMINATING SETS | LONG BELT COVERAGE | COMPUTER SCIENCE, THEORY & METHODS | NODE PLACEMENT | Remote sensors | Wireless networks | Energy management

Greedy algorithms | Wireless sensor networks | Strips | uniform sensing range | multi-cover | Approximation algorithms | maximum lifetime | weight | Sensors | Partitioning algorithms | Approximation algorithm | IEEE transactions | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHMS | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TARGET COVERAGE | CONNECTED DOMINATING SETS | LONG BELT COVERAGE | COMPUTER SCIENCE, THEORY & METHODS | NODE PLACEMENT | Remote sensors | Wireless networks | Energy management

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2012, Volume 28, Issue 1, pp. 1 - 55

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in...

k -Tuple domination | l -Total k -domination | Connected k -domination | k -Independence | k -Irredundance | Mathematics | k -Star-forming | Engineering Design | Combinatorics | k -Domination | 05C69 | l-Total k-domination | k-Domination | k-Star-forming | k-Irredundance | Connected k-domination | k-Independence | k-Tuple domination | P-DOMINATION | F-DOMINATION | IRREDUNDANCE | EQUAL DOMINATION | TRANSVERSAL NUMBERS | CONJECTURE | MATHEMATICS | TREES | BOUNDS | 2-DOMINATION NUMBER | TUPLE DOMINATION | Graphs | Star & galaxy formation | Integers | Combinatorial analysis

k -Tuple domination | l -Total k -domination | Connected k -domination | k -Independence | k -Irredundance | Mathematics | k -Star-forming | Engineering Design | Combinatorics | k -Domination | 05C69 | l-Total k-domination | k-Domination | k-Star-forming | k-Irredundance | Connected k-domination | k-Independence | k-Tuple domination | P-DOMINATION | F-DOMINATION | IRREDUNDANCE | EQUAL DOMINATION | TRANSVERSAL NUMBERS | CONJECTURE | MATHEMATICS | TREES | BOUNDS | 2-DOMINATION NUMBER | TUPLE DOMINATION | Graphs | Star & galaxy formation | Integers | Combinatorial analysis

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 4/2017, Volume 33, Issue 3, pp. 924 - 933

Let $$k\ge 2, p\ge 1, q\ge 0$$ k ≥ 2 , p ≥ 1 , q ≥ 0 be integers. We prove that every $$(4kp-2p+2q)$$ ( 4 k p - 2 p + 2 q ) -connected graph contains p...

Convex and Discrete Geometry | Spanning tree | k -Rigid | Essentially connected | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Orientation | Optimization | k-Rigid | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RIGIDITY | ORIENTATIONS | GRAPHS

Convex and Discrete Geometry | Spanning tree | k -Rigid | Essentially connected | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Orientation | Optimization | k-Rigid | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RIGIDITY | ORIENTATIONS | GRAPHS

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 05/2018, Volume 88, Issue 1, pp. 146 - 153

For minimally k‐connected graphs on n vertices, Mader proved a tight lower bound for the number |Vk| of vertices of degree k in dependence on n and k. Oxley...

minimally k‐connected graphs | tight | lower bounds | vertices of degree k | minimally k-connected graphs | MATHEMATICS

minimally k‐connected graphs | tight | lower bounds | vertices of degree k | minimally k-connected graphs | MATHEMATICS

Journal Article

IEEE Transactions on Industrial Electronics, ISSN 0278-0046, 02/2015, Volume 62, Issue 2, pp. 1317 - 1328

Aiming at finding the k nodes with the highest readings among sensor nodes, top-k query is a very important and useful query in wireless sensor networks...

Wireless sensor networks | Energy consumption | Base stations | Interference | Educational institutions | Data models | Erbium | duty-cycled WSNs (D-WSNs) | data replication (DR) | top-k query | WSNs | Always-on wireless sensor networks (A-WSNs) | neighborhood (CKN) | connected k | connected k(c)-neighborhood (CKN) | INSTRUMENTS & INSTRUMENTATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Query processing | Analysis | Data replication | Sensors | Software upgrading | Industrial electronics | Remote sensors | Simulation | Wireless networks | Accessibility | Energy conservation | Cost analysis

Wireless sensor networks | Energy consumption | Base stations | Interference | Educational institutions | Data models | Erbium | duty-cycled WSNs (D-WSNs) | data replication (DR) | top-k query | WSNs | Always-on wireless sensor networks (A-WSNs) | neighborhood (CKN) | connected k | connected k(c)-neighborhood (CKN) | INSTRUMENTS & INSTRUMENTATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Query processing | Analysis | Data replication | Sensors | Software upgrading | Industrial electronics | Remote sensors | Simulation | Wireless networks | Accessibility | Energy conservation | Cost analysis

Journal Article

6.
Full Text
An O(log 2 k)-Approximation algorithm for the k-vertex connected spanning Subgraph problem

SIAM Journal on Computing, ISSN 0097-5397, 2012, Volume 41, Issue 5, pp. 1095 - 1109

We present an $O(\log^2{k})$-approximation algorithm for the problem of finding a $k$-vertex connected spanning subgraph of minimum cost, where $n$ is the...

Network design | Vertex-connectivity | Approximation algorithm | K-connected graph | Subroutines | Algorithms | Approximation | Mathematical analysis | Minimum cost | Graphs | Mathematical models | Optimization

Network design | Vertex-connectivity | Approximation algorithm | K-connected graph | Subroutines | Algorithms | Approximation | Mathematical analysis | Minimum cost | Graphs | Mathematical models | Optimization

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2008, Volume 45, Issue 4, pp. 923 - 952

In this paper several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the...

Computer topology | Khalimsky continuity | K-(k | KD-(k | continuity | k | Digital (k | MATHEMATICS, APPLIED | K-(k, k)-continuity | K-(k, k)-homeomorphism | CLOSED SURFACES | digital (k, k)-continuity | Khalimsky line | CURVES | CONNECTED SUM | MATHEMATICS | KD-(k, k)-continuity | KD-(k, k)-homeomorphism | Khalimsky n-space | (k, k)-homeomorphism | DIGITAL FUNDAMENTAL GROUP | (k, k)-continuity | computer topology

Computer topology | Khalimsky continuity | K-(k | KD-(k | continuity | k | Digital (k | MATHEMATICS, APPLIED | K-(k, k)-continuity | K-(k, k)-homeomorphism | CLOSED SURFACES | digital (k, k)-continuity | Khalimsky line | CURVES | CONNECTED SUM | MATHEMATICS | KD-(k, k)-continuity | KD-(k, k)-homeomorphism | Khalimsky n-space | (k, k)-homeomorphism | DIGITAL FUNDAMENTAL GROUP | (k, k)-continuity | computer topology

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2014, Volume 166, pp. 263 - 268

A digraph is called rooted -edge-connected if it has a root node such that there exist arc-disjoint paths from to every other node and there is a path from...

Highly [formula omitted]-tree-connected | Orientation | Rooted edge-connectivity | Highly k-tree-connected | MATHEMATICS, APPLIED | GRAPHS | Algorithms | Mathematical analysis | Roots | Rigid-body dynamics | Running | Graphs | Graph theory

Highly [formula omitted]-tree-connected | Orientation | Rooted edge-connectivity | Highly k-tree-connected | MATHEMATICS, APPLIED | GRAPHS | Algorithms | Mathematical analysis | Roots | Rigid-body dynamics | Running | Graphs | Graph theory

Journal Article

Discrete Mathematics, ISSN 0012-365X, 12/2019, Volume 342, Issue 12, p. 111598

An edge of a -connected graph is said to be -contractible if the contraction of the edge results in a -connected graph. For a graph and a vertex of , let be...

[formula omitted]-connected graph | Contraction-critically [formula omitted]-connected | Neighborhood | MATHEMATICS | k-connected graph | Contraction-critically k-connected

[formula omitted]-connected graph | Contraction-critically [formula omitted]-connected | Neighborhood | MATHEMATICS | k-connected graph | Contraction-critically k-connected

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2016, Volume 31, Issue 2, pp. 669 - 685

In this paper we give improved approximation algorithms for some network design problems. In the bounded-diameter or shallow-light $$k$$ k -Steiner tree...

k$$ k -edge connected | Network design | Steiner tree | Convex and Discrete Geometry | Approximation algorithms | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Combinatorial optimization | Optimization

k$$ k -edge connected | Network design | Steiner tree | Convex and Discrete Geometry | Approximation algorithms | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Combinatorial optimization | Optimization

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2018, Volume 325, pp. 332 - 339

A connected graph is said to be -connected if it has more than vertices and remains connected whenever fewer than vertices are removed. Feng et al. (2017)...

Signless Laplacian spectral radius | K-connected | Distance spectral radius | Distance signless Laplacian spectral radius | MATHEMATICS, APPLIED | TRACEABLE GRAPHS | TREES | HAMILTONIAN PROPERTIES | LAPLACIAN SPECTRAL-RADIUS | HARARY INDEX | WIENER POLARITY INDEX

Signless Laplacian spectral radius | K-connected | Distance spectral radius | Distance signless Laplacian spectral radius | MATHEMATICS, APPLIED | TRACEABLE GRAPHS | TREES | HAMILTONIAN PROPERTIES | LAPLACIAN SPECTRAL-RADIUS | HARARY INDEX | WIENER POLARITY INDEX

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2017, Volume 311, pp. 223 - 227

A total-colored graph is total rainbow connected if any two vertices are connected by a path whose edges and inner vertices have distinct colors. A graph is...

Total rainbow coloring | Total rainbow connection number | Minimally total rainbow k-connected graph | MATHEMATICS, APPLIED | NUMBERS | COMPLEXITY

Total rainbow coloring | Total rainbow connection number | Minimally total rainbow k-connected graph | MATHEMATICS, APPLIED | NUMBERS | COMPLEXITY

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2016, Volume 205, pp. 101 - 108

A vertex subset of a connected graph is called a connected -path vertex cover ( ) if every path on vertices contains at least one vertex from , and the...

Tree | Connected [formula omitted]-path vertex cover | Approximation algorithm | Girth | Weight | Connected k-path vertex cover | Algorithms

Tree | Connected [formula omitted]-path vertex cover | Approximation algorithm | Girth | Weight | Connected k-path vertex cover | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2014, Volume 174, pp. 92 - 101

Let be a positive integer and be a -connected graph. In 2009, Chartrand, Johns, McKeon, and Zhang introduced the of . An edge-coloured path is if its edges...

Graph colouring | Rainbow (vertex) connection number | [formula omitted]-connected | k-connected | MATHEMATICS, APPLIED

Graph colouring | Rainbow (vertex) connection number | [formula omitted]-connected | k-connected | MATHEMATICS, APPLIED

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 08/2018, Volume 88, Issue 4, pp. 592 - 605

Let k and ℓ be positive integers. A cycle with two blocks c(k,ℓ) is a digraph obtained by an orientation of an undirected cycle, which consists of two...

chromatic number | digraph coloring | strongly connected digraph | cycle with two blocks | MATHEMATICS | TREES | TOURNAMENTS | PATHS | CONJECTURE

chromatic number | digraph coloring | strongly connected digraph | cycle with two blocks | MATHEMATICS | TREES | TOURNAMENTS | PATHS | CONJECTURE

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2015, Volume 181, pp. 1 - 10

Given a simple undirected graph G and a positive integer k, the k-forcing number of G, denoted (G), is the minimum number of vertices that need to be initially...

Nullity | Connected dominating sets | Connected domination number | k-forcing number | Zero forcing set | Zero forcing number | k-independence number | Rank | k-forcing | MATHEMATICS, APPLIED | INDEPENDENCE | SETS | DOMINATION

Nullity | Connected dominating sets | Connected domination number | k-forcing number | Zero forcing set | Zero forcing number | k-independence number | Rank | k-forcing | MATHEMATICS, APPLIED | INDEPENDENCE | SETS | DOMINATION

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2009, Volume 410, Issue 19, pp. 1749 - 1764

We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in...

Random geometric graph | Clustering | Connected component | Neighborhood graph | COMPUTER SCIENCE, THEORY & METHODS | CONNECTIVITY | Algorithms

Random geometric graph | Clustering | Connected component | Neighborhood graph | COMPUTER SCIENCE, THEORY & METHODS | CONNECTIVITY | Algorithms

Journal Article

ALGEBRAIC GEOMETRY, ISSN 2313-1691, 03/2019, Volume 6, Issue 2, pp. 196 - 233

A k-differential on a Riemann surface is a section of the kth power of the canonical line bundle. Loci of k-differentials with prescribed number and...

CONNECTED COMPONENTS | MATHEMATICS | compactification | flat geometry | QUADRATIC-DIFFERENTIALS | k-differentials | strata | deformation | MODULI SPACES | SURFACES

CONNECTED COMPONENTS | MATHEMATICS | compactification | flat geometry | QUADRATIC-DIFFERENTIALS | k-differentials | strata | deformation | MODULI SPACES | SURFACES

Journal Article

Sensors (Switzerland), ISSN 1424-8220, 01/2016, Volume 16, Issue 1, p. 104

Coverage and connectivity are two important performance evaluation indices for wireless sensor networks (WSNs). In this paper, we focus on the connected target...

Connected cover set | Connectivity | Heterogeneous wireless sensor networks (HWSNs) | K-coverage | CHEMISTRY, ANALYTICAL | INSTRUMENTS & INSTRUMENTATION | heterogeneous wireless sensor networks (HWSNs) | connectivity | connected cover set | k-coverage | LIFETIME | ENGINEERING, ELECTRICAL & ELECTRONIC

Connected cover set | Connectivity | Heterogeneous wireless sensor networks (HWSNs) | K-coverage | CHEMISTRY, ANALYTICAL | INSTRUMENTS & INSTRUMENTATION | heterogeneous wireless sensor networks (HWSNs) | connectivity | connected cover set | k-coverage | LIFETIME | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 12/2014, Volume 173, Issue 1, pp. 65 - 82

In Pralle and Shpectorov (Adv Geom 7(1):1–17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that...

Geometry | Simply connected | Affine | Biaffine | 51E24 | Mathematics | 20F05 | Flag-transitive | Hyperplane | Polar space

Geometry | Simply connected | Affine | Biaffine | 51E24 | Mathematics | 20F05 | Flag-transitive | Hyperplane | Polar space

Journal Article

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