Discrete Applied Mathematics, ISSN 0166-218X, 03/2019, Volume 257, pp. 158 - 174

.... Given a graph class H, the H-Square Root problem asks for the recognition of the squares of graphs in H...

Cactus-block graphs | Square root of a graph | Cycle-power graphs | Clique-separator decomposition | Cut-vertices | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | POWERS | Algorithms | Research institutes | Apexes | Roots | Graphs | Trees (mathematics) | Graph theory | Polynomials | Decomposition | Recognition | Data Structures and Algorithms | Computer Science | Computational Complexity | Discrete Mathematics

Cactus-block graphs | Square root of a graph | Cycle-power graphs | Clique-separator decomposition | Cut-vertices | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | POWERS | Algorithms | Research institutes | Apexes | Roots | Graphs | Trees (mathematics) | Graph theory | Polynomials | Decomposition | Recognition | Data Structures and Algorithms | Computer Science | Computational Complexity | Discrete Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2014, Volume 168, pp. 34 - 39

Let G be a graph class. The square root of G contains all graphs whose squares belong in G...

Carving-width | Square roots of graphs | Graph minors | Branch-width | MATHEMATICS, APPLIED | CONTAINMENT | ALGORITHMS | Algorithms | Graphs | Mathematical analysis | Roots | Recognition | Computer Science | Discrete Mathematics

Carving-width | Square roots of graphs | Graph minors | Branch-width | MATHEMATICS, APPLIED | CONTAINMENT | ALGORITHMS | Algorithms | Graphs | Mathematical analysis | Roots | Recognition | Computer Science | Discrete Mathematics

Journal Article

Algorithmica, ISSN 0178-4617, 2/2012, Volume 62, Issue 1, pp. 38 - 53

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H...

Recognition algorithms | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Graph powers | Computer Science | NP-completeness | Theory of Computation | Algorithm Analysis and Problem Complexity | Graph roots | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SQUARE | ALGORITHMS | POWERS | Computer science

Recognition algorithms | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Graph powers | Computer Science | NP-completeness | Theory of Computation | Algorithm Analysis and Problem Complexity | Graph roots | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SQUARE | ALGORITHMS | POWERS | Computer science

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, pp. 93 - 101

A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2...

Square root | Polynomial algorithm | Bounded degree graph | MATHEMATICS, APPLIED | SPLIT GRAPHS | LOGIC | Computer Science | Computational Complexity

Square root | Polynomial algorithm | Bounded degree graph | MATHEMATICS, APPLIED | SPLIT GRAPHS | LOGIC | Computer Science | Computational Complexity

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2013, Volume 161, Issue 10-11, pp. 1538 - 1545

A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H...

Linear time algorithm | Chordal graph | Split graph | Trivially perfect graph | Threshold graph | Square root of a graph | Square of a graph | MATHEMATICS, APPLIED | NLC-WIDTH | POWERS | Algorithms | Thresholds | Computation | Roots | Graphs | Mathematical models | Computing time | Structural analysis

Linear time algorithm | Chordal graph | Split graph | Trivially perfect graph | Threshold graph | Square root of a graph | Square of a graph | MATHEMATICS, APPLIED | NLC-WIDTH | POWERS | Algorithms | Thresholds | Computation | Roots | Graphs | Mathematical models | Computing time | Structural analysis

Journal Article

Algorithmica, ISSN 0178-4617, 7/2019, Volume 81, Issue 7, pp. 2795 - 2828

Deciding if a graph has a square root is a classical problem, which has been studied extensively both from graph-theoretic and algorithmic perspective...

Computer Systems Organization and Communication Networks | Outerplanar graphs | Algorithms | Graphs of pathwidth 2 | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Data Structures and Information Theory | Computer science

Computer Systems Organization and Communication Networks | Outerplanar graphs | Algorithms | Graphs of pathwidth 2 | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Data Structures and Information Theory | Computer science

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 08/2017, Volume 689, pp. 36 - 47

A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are at distance 2 from each...

Square root | k-apex graphs | Linear kernel | COMPUTER SCIENCE, THEORY & METHODS | SPLIT

Square root | k-apex graphs | Linear kernel | COMPUTER SCIENCE, THEORY & METHODS | SPLIT

Journal Article

Algorithmica, ISSN 0178-4617, 2/2015, Volume 71, Issue 2, pp. 471 - 495

... at most p. Given an n-node m-edge graph G and a positive integer p, the p-th tree root problem asks for a tree T, if any, such that G=T p...

Graph root | Minimal node separator | Tree root | Graph power | Chordal graph | Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Maximal clique | Mathematics of Computing | Computer Science | Tree power | Algorithm Analysis and Problem Complexity | INTERVAL | MATHEMATICS, APPLIED | SQUARE | CHROMATIC NUMBER | INDEPENDENT SETS | GRAPH POWERS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SEPARATORS | Computer science

Graph root | Minimal node separator | Tree root | Graph power | Chordal graph | Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Maximal clique | Mathematics of Computing | Computer Science | Tree power | Algorithm Analysis and Problem Complexity | INTERVAL | MATHEMATICS, APPLIED | SQUARE | CHROMATIC NUMBER | INDEPENDENT SETS | GRAPH POWERS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SEPARATORS | Computer science

Journal Article

Theory of Computing Systems, ISSN 1432-4350, 8/2018, Volume 62, Issue 6, pp. 1409 - 1426

A graph H is a square root of a graph G, or equivalently, G is the square of H, if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2...

Theory of Computation | Clique number | Square root | Computer Science | Cactus | Treewidth | MATHEMATICS | SQUARE ROOTS | COMPUTER SCIENCE, THEORY & METHODS | SPLIT GRAPHS | Computer science | Computational mathematics | Graph theory | Polynomials | Algorithms

Theory of Computation | Clique number | Square root | Computer Science | Cactus | Treewidth | MATHEMATICS | SQUARE ROOTS | COMPUTER SCIENCE, THEORY & METHODS | SPLIT GRAPHS | Computer science | Computational mathematics | Graph theory | Polynomials | Algorithms

Journal Article

10.
Full Text
Polynomial time recognition of squares of Ptolemaic graphs and 3-sun-free split graphs

Theoretical Computer Science, ISSN 0304-3975, 10/2015, Volume 602, pp. 39 - 49

.... Then G is called a square root of G2. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a chordal graph or even a split graph...

Square of Ptolemaic graph | Square of graph | Recognition algorithm | Square of split graph | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | POWERS | Algorithms | Graphs | Polynomials | Graph theory | Roots | Recognition

Square of Ptolemaic graph | Square of graph | Recognition algorithm | Square of split graph | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | POWERS | Algorithms | Graphs | Polynomials | Graph theory | Roots | Recognition

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2014, Volume 173, pp. 83 - 91

The square of a graph G, denoted by G2, is the graph obtained from G by putting an edge between two distinct vertices whenever their distance in G is at most...

Linear time algorithm | The square of a graph | Line graph | MATHEMATICS, APPLIED | ROOTS | Algorithms | Mathematical analysis | Graphs

Linear time algorithm | The square of a graph | Line graph | MATHEMATICS, APPLIED | ROOTS | Algorithms | Mathematical analysis | Graphs

Journal Article

ALGORITHMICA, ISSN 0178-4617, 07/2019, Volume 81, Issue 7, pp. 2795 - 2828

Deciding if a graph has a square root is a classical problem, which has been studied extensively both from graph-theoretic and algorithmic perspective...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Outerplanar graphs | Graphs of pathwidth 2 | Graph square root

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Outerplanar graphs | Graphs of pathwidth 2 | Graph square root

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 10/2016, Volume 648, pp. 26 - 33

.... Then G is called a square root of G2. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a split graph...

Square of graphs | Square of split graphs | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Theorems | Roots | Graphs | Polynomials | Graph theory | Cases (containers) | Dichotomies

Square of graphs | Square of split graphs | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Theorems | Roots | Graphs | Polynomials | Graph theory | Cases (containers) | Dichotomies

Journal Article

Mathematical problems in engineering, ISSN 1024-123X, 5/2019, Volume 2019, pp. 1 - 25

In order to realize the multithreshold segmentation of images, an improved segmentation algorithm based on graph cut theory using artificial bee colony is proposed...

THRESHOLDING METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Root-mean-square errors | Image segmentation | Algorithms | Search algorithms | Entropy (Information theory) | Cost function | Swarm intelligence | Weighting functions | Pixels | Image reconstruction | Signal to noise ratio

THRESHOLDING METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Root-mean-square errors | Image segmentation | Algorithms | Search algorithms | Entropy (Information theory) | Cost function | Swarm intelligence | Weighting functions | Pixels | Image reconstruction | Signal to noise ratio

Journal Article

Algorithmica, ISSN 0178-4617, 2/2016, Volume 74, Issue 2, pp. 602 - 629

... : testing whether a connected $$n$$ n -vertex graph with $$m$$ m edges has a square root with at most $$n-1+k$$ n - 1...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Generalized kernel | Parameterized complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computational Complexity

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Generalized kernel | Parameterized complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computational Complexity

Journal Article

Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 06/2016, Volume 53, pp. 4.1 - 4.14

Conference Proceeding

Computer Aided Geometric Design, ISSN 0167-8396, 08/2017, Volume 56, pp. 52 - 66

.... Hence, we deal with rational, elliptic or hyperelliptic curves that are birational to plane curves in the Weierstrass form and thus they are square-root parameterizable...

Weierstrass form | Hyperelliptic curves | Rational approximation | Topological graph | Square-root parameterization | OFFSETS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SPACE-CURVES | CANAL SURFACES | BISECTOR | Analysis | Algorithms

Weierstrass form | Hyperelliptic curves | Rational approximation | Topological graph | Square-root parameterization | OFFSETS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SPACE-CURVES | CANAL SURFACES | BISECTOR | Analysis | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 02/2017, Volume 218, pp. 98 - 112

For a connected graph G=(V(G),E(G)) and two disjoint subsets of V(G) A={α1,…,αk} and B={β1,…,βk}, a paired (many-to-many) k-disjoint path cover of G joining A and B is a vertex-disjoint path cover...

Cube of graph | Unicyclic graph | Disjoint path cover | Spanning tree | Hamiltonian path | Linear-time algorithm | SHORT PROOF | MATHEMATICS, APPLIED | SQUARE ROOTS | FLEISCHNERS THEOREM | POWERS | HYPERCUBES | RECURSIVE CIRCULANTS G(2(M) | FAULTY ELEMENTS | PARTITIONS | EDGES | Algorithms | Computer science

Cube of graph | Unicyclic graph | Disjoint path cover | Spanning tree | Hamiltonian path | Linear-time algorithm | SHORT PROOF | MATHEMATICS, APPLIED | SQUARE ROOTS | FLEISCHNERS THEOREM | POWERS | HYPERCUBES | RECURSIVE CIRCULANTS G(2(M) | FAULTY ELEMENTS | PARTITIONS | EDGES | Algorithms | Computer science

Journal Article

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, ISSN 1057-7122, 12/2002, Volume 49, Issue 12, pp. 1702 - 1712

A new systematic design procedure for square-root-domain (/spl radic/x-domain) circuits, which is based on the signal flow graph (SFG...

Low pass filters | Circuit simulation | Prototypes | Chebyshev approximation | Circuit synthesis | Complexity theory | Flow graphs | Signal synthesis | Signal design | Immune system | Active filter | Translinear circuits | Square-root-domain (√x-domain) circuits | Analog integrated circuits | INTEGRATOR | square-root-domain (root x-domain) circuits | translinear circuits | analog integrated circuits | FILTERS | active filter | PRINCIPLE | STATE-SPACE | ENGINEERING, ELECTRICAL & ELECTRONIC

Low pass filters | Circuit simulation | Prototypes | Chebyshev approximation | Circuit synthesis | Complexity theory | Flow graphs | Signal synthesis | Signal design | Immune system | Active filter | Translinear circuits | Square-root-domain (√x-domain) circuits | Analog integrated circuits | INTEGRATOR | square-root-domain (root x-domain) circuits | translinear circuits | analog integrated circuits | FILTERS | active filter | PRINCIPLE | STATE-SPACE | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Nanomaterials, ISSN 2079-4991, 11/2017, Volume 7, Issue 11, p. 386

...) of 0.863 and test root-mean-square error (RMSE) of 0.0461. The results demonstrate the capability of encoding CNT information into spectral moments of the Raman star graphs (SG...

Carbon nanotubes | Cytotoxicity | Spectral moments | Graph theory | Mitochondria oxygen mass flux | Raman spectroscopy | mitochondria oxygen mass flux | CELLS | APOPTOSIS | PERTURBATIONS | SEQUENCES | graph theory | MATERIALS SCIENCE, MULTIDISCIPLINARY | CLASSIFICATION | NANOSCIENCE & NANOTECHNOLOGY | PREDICTION | carbon nanotubes | SPECTROSCOPY | RESPIRATION | spectral moments | PROTEINS | cytotoxicity | TOPOLOGICAL INDEXES | Perturbation theory | Root-mean-square errors | Raman spectra | Oxygen | Nanotubes | Oxygen consumption | Learning algorithms | Mitochondria | Dynamic tests | Polarography | Risk assessment | Machine learning | Predictions | Mathematical models | Nanotechnology

Carbon nanotubes | Cytotoxicity | Spectral moments | Graph theory | Mitochondria oxygen mass flux | Raman spectroscopy | mitochondria oxygen mass flux | CELLS | APOPTOSIS | PERTURBATIONS | SEQUENCES | graph theory | MATERIALS SCIENCE, MULTIDISCIPLINARY | CLASSIFICATION | NANOSCIENCE & NANOTECHNOLOGY | PREDICTION | carbon nanotubes | SPECTROSCOPY | RESPIRATION | spectral moments | PROTEINS | cytotoxicity | TOPOLOGICAL INDEXES | Perturbation theory | Root-mean-square errors | Raman spectra | Oxygen | Nanotubes | Oxygen consumption | Learning algorithms | Mitochondria | Dynamic tests | Polarography | Risk assessment | Machine learning | Predictions | Mathematical models | Nanotechnology

Journal Article