Graphs and Combinatorics, ISSN 0911-0119, 1/2017, Volume 33, Issue 1, pp. 85 - 102

In this paper we work to classify which of the (n, k)-star graphs, denoted by $$S_{n,k}$$ S n , k , are Cayley graphs. Although the complete classification is...

(n, k)-star graphs | Mathematics | Engineering Design | Cayley graphs | Combinatorics | Vertex-forwarding index | Interconnection networks | MATHEMATICS | HYPER HAMILTONIAN LACEABILITY | STAR GRAPHS | TREES | CONNECTIVITY | ALGORITHM | FORWARDING INDEX | NETWORKS | Texts | Graphs | Combinatorial analysis | Shortest-path problems | Classification

(n, k)-star graphs | Mathematics | Engineering Design | Cayley graphs | Combinatorics | Vertex-forwarding index | Interconnection networks | MATHEMATICS | HYPER HAMILTONIAN LACEABILITY | STAR GRAPHS | TREES | CONNECTIVITY | ALGORITHM | FORWARDING INDEX | NETWORKS | Texts | Graphs | Combinatorial analysis | Shortest-path problems | Classification

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 2, pp. 906 - 937

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open...

Symmetry reduction | Dirac structures | Network dynamics | Stability | Hamiltonian dynamics | Physical systems | MATHEMATICS, APPLIED | symmetry reduction | physical systems | CONSERVING PHYSICAL SYSTEMS | MULTIAGENT SYSTEMS | network dynamics | FORMULATION | PASSIVITY | MECHANICAL NETWORKS | DYNAMICS | stability | AUTOMATION & CONTROL SYSTEMS | Networks | Dynamics | Control systems | Graphs | Mathematical models | Graph theory | Dynamical systems | Optimization | Chemical engineering | Chemical and Process Engineering | Computer Science | Automatic Control Engineering | Engineering Sciences | Chemical Sciences | Automatic

Symmetry reduction | Dirac structures | Network dynamics | Stability | Hamiltonian dynamics | Physical systems | MATHEMATICS, APPLIED | symmetry reduction | physical systems | CONSERVING PHYSICAL SYSTEMS | MULTIAGENT SYSTEMS | network dynamics | FORMULATION | PASSIVITY | MECHANICAL NETWORKS | DYNAMICS | stability | AUTOMATION & CONTROL SYSTEMS | Networks | Dynamics | Control systems | Graphs | Mathematical models | Graph theory | Dynamical systems | Optimization | Chemical engineering | Chemical and Process Engineering | Computer Science | Automatic Control Engineering | Engineering Sciences | Chemical Sciences | Automatic

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2019, Volume 265, pp. 40 - 55

An incidence of a graph is a pair where is a vertex of and is an edge of incident with . Two incidences and of are adjacent whenever (i) , or (ii) , or...

Incidence colouring | List colouring | Hamiltonian cubic graph | Incidence list colouring | Square grid | Halin graph | INCIDENCE CHROMATIC NUMBER | MATHEMATICS, APPLIED | INCIDENCE COLORING CONJECTURE | Coloring | Graphs | Mapping | Upper bounds | Incidence | Computer Science | Discrete Mathematics

Incidence colouring | List colouring | Hamiltonian cubic graph | Incidence list colouring | Square grid | Halin graph | INCIDENCE CHROMATIC NUMBER | MATHEMATICS, APPLIED | INCIDENCE COLORING CONJECTURE | Coloring | Graphs | Mapping | Upper bounds | Incidence | Computer Science | Discrete Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 02/2016, Volume 200, pp. 79 - 94

For an integer and for with , an -trail-system of is a subgraph consisting of edge-disjoint -trails. A graph is if for any with , has a spanning -trail-system....

Edge-connectivity | Collapsible graphs | Edge-disjoint trails | The supereulerian width of a graph | Eulerian-connected graphs | Supereulerian graphs with width [formula omitted] | [formula omitted]-collapsible graphs | Supereulerian graphs | Supereulerian graphs with width s | s-collapsible graphs | MATHEMATICS, APPLIED | TRAILS | CONNECTIVITY | EULERIAN GRAPHS | The supereulerian width of a graph s-collapsible graphs | DISJOINT SPANNING-TREES | HAMILTONIAN LINE GRAPHS

Edge-connectivity | Collapsible graphs | Edge-disjoint trails | The supereulerian width of a graph | Eulerian-connected graphs | Supereulerian graphs with width [formula omitted] | [formula omitted]-collapsible graphs | Supereulerian graphs | Supereulerian graphs with width s | s-collapsible graphs | MATHEMATICS, APPLIED | TRAILS | CONNECTIVITY | EULERIAN GRAPHS | The supereulerian width of a graph s-collapsible graphs | DISJOINT SPANNING-TREES | HAMILTONIAN LINE GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 11/2019, Volume 342, Issue 11, pp. 3006 - 3016

For an integer , a graph is -hamiltonian if for any vertex subset with , is hamiltonian, and is -hamiltonian connected if for any vertex subset with , is...

Line graphs | Claw-free graphs | [formula omitted]-hamiltonian graphs | s-hamiltonian graphs | MATHEMATICS | CONNECTEDNESS

Line graphs | Claw-free graphs | [formula omitted]-hamiltonian graphs | s-hamiltonian graphs | MATHEMATICS | CONNECTEDNESS

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 01/2019, Volume 54, Issue 1, pp. 148 - 186

We investigate the asymptotic structure of a random perfect graph Pn sampled uniformly from the set of perfect graphs on vertex set {1,…,n}. Our approach is...

perfect graphs | edge‐coloring | Hamiltonian | Clique‐coloring | graph limits | Clique-coloring | edge-coloring | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Graph coloring | Asymptotic properties

perfect graphs | edge‐coloring | Hamiltonian | Clique‐coloring | graph limits | Clique-coloring | edge-coloring | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Graph coloring | Asymptotic properties

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2019, p. 111663

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 7/2019, Volume 35, Issue 4, pp. 827 - 836

A hamiltonian walk in a digraph D is a closed spanning directed walk of D with minimum length. The length of a hamiltonian walk in D is called the hamiltonian...

05C45 | Hamiltonian number | Hamiltonian spectrum | Mathematics | Engineering Design | Combinatorics | Orientation | 05C69 | 05C38 | MATHEMATICS | Integers | Graphs | Graph theory

05C45 | Hamiltonian number | Hamiltonian spectrum | Mathematics | Engineering Design | Combinatorics | Orientation | 05C69 | 05C38 | MATHEMATICS | Integers | Graphs | Graph theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 192 - 206

Invoking Steinitz’ Theorem, in the following a shall be a 3-connected planar graph. From around 1880 till 1946 Tait’s conjecture that cubic polyhedra are...

Polyhedron | Planar | Non-hamiltonian | 3-connected | Non-traceable | Regular graph | CIRCUITS | MATHEMATICS, APPLIED | PLANAR GRAPHS | LESS

Polyhedron | Planar | Non-hamiltonian | 3-connected | Non-traceable | Regular graph | CIRCUITS | MATHEMATICS, APPLIED | PLANAR GRAPHS | LESS

Journal Article

01/2017, ISBN 0824787900

Pairwise balanced design | Vertex disjoint union | Hamiltonian cycle | Complete bipartite graph | Complete graph | Cleavage unit | Latin square | Multiple edges | Disjoint edges | Group divisible design | Positive integer | Vertex V | Triple system | Clique partition | Maximum matching | Independent set | Bipartite graph | Block size | Edge set | Regular graph

Book

Discrete Applied Mathematics, ISSN 0166-218X, 09/2019

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 01/2014, Volume 516, pp. 28 - 39

The -star graphs are a generalized version of -star graphs, which belong to the class of Cayley graphs, and have been recognized as an attractive alternative...

[formula omitted]-star graph | Weak-pancyclicity | Fault-tolerance | Cayley graph | Cycle embedding | (n, k) -star graph | STAR GRAPHS | CHIP-MULTIPROCESSOR | CUBES | EDGE-FAULT-TOLERANT | HAMILTONIAN-CONNECTIVITY | HYPERCUBES | (n, k)-star graph | TOURNAMENTS | BIPANCYCLICITY | COMPUTER SCIENCE, THEORY & METHODS | PANCONNECTIVITY | (N,K)-STAR GRAPHS | Computer science

[formula omitted]-star graph | Weak-pancyclicity | Fault-tolerance | Cayley graph | Cycle embedding | (n, k) -star graph | STAR GRAPHS | CHIP-MULTIPROCESSOR | CUBES | EDGE-FAULT-TOLERANT | HAMILTONIAN-CONNECTIVITY | HYPERCUBES | (n, k)-star graph | TOURNAMENTS | BIPANCYCLICITY | COMPUTER SCIENCE, THEORY & METHODS | PANCONNECTIVITY | (N,K)-STAR GRAPHS | Computer science

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 1092 - 1097

For a connected graph not isomorphic to a path, a cycle or a , let pc denote the smallest integer such that the th iterated line graph is panconnected. A path...

Panconnected index of graphs | Iterated line graphs | Panconnectedness | MATHEMATICS | LINE-GRAPHS | HAMILTONIAN INDEX

Panconnected index of graphs | Iterated line graphs | Panconnectedness | MATHEMATICS | LINE-GRAPHS | HAMILTONIAN INDEX

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 08/2017, Volume 690, pp. 26 - 58

The Hamiltonian path problem for general grid graphs is NP-complete. In this paper, we give the necessary conditions for the existence of a Hamiltonian path...

Grid graph | NP-complete | Rectangular grid graphs with a rectangular hole | Hamiltonian cycle | Hamiltonian path | hole | CYCLES | PATHS | Rectangular grid graphs with a rectangular | COMPUTER SCIENCE, THEORY & METHODS | CIRCUIT PROBLEM | Computer science | Algorithms

Grid graph | NP-complete | Rectangular grid graphs with a rectangular hole | Hamiltonian cycle | Hamiltonian path | hole | CYCLES | PATHS | Rectangular grid graphs with a rectangular | COMPUTER SCIENCE, THEORY & METHODS | CIRCUIT PROBLEM | Computer science | Algorithms

Journal Article

BMC Bioinformatics, ISSN 1471-2105, 06/2016, Volume 17, Issue 1, p. 237

Background: Next Generation Sequencing (NGS) has dramatically enhanced our ability to sequence genomes, but not to assemble them. In practice, many published...

De Bruijn graph | Path | Genomics | Read mapping | Hamiltonian path | NP-complete | NGS | Assembly | Sequence graph | ACCURATE | BIOCHEMICAL RESEARCH METHODS | REPRESENTATION | path | ALIGNMENT | GENOMES | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EFFICIENT | Algorithms | Escherichia coli - genetics | Humans | Contig Mapping | High-Throughput Nucleotide Sequencing | Genome, Human | Genomics - methods | Sequence Analysis, DNA | Usage | Research | Nucleotide sequencing | Methods | DNA sequencing | Bioinformatics | Computer Science

De Bruijn graph | Path | Genomics | Read mapping | Hamiltonian path | NP-complete | NGS | Assembly | Sequence graph | ACCURATE | BIOCHEMICAL RESEARCH METHODS | REPRESENTATION | path | ALIGNMENT | GENOMES | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EFFICIENT | Algorithms | Escherichia coli - genetics | Humans | Contig Mapping | High-Throughput Nucleotide Sequencing | Genome, Human | Genomics - methods | Sequence Analysis, DNA | Usage | Research | Nucleotide sequencing | Methods | DNA sequencing | Bioinformatics | Computer Science

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2017, Volume 340, Issue 6, pp. 1210 - 1226

Line graphs constitute a rich and well-studied class of graphs. In this paper, we focus on three different topics related to line graphs of subcubic...

Min-max theorems | [formula omitted]-completeness | Line graph | Approximation hardness | Independence number | Matching number | NP-completeness | CLAW | RATIO | MATCHINGS | HAMILTONIAN PATH PROBLEM | INDEPENDENT SETS | FEEDBACK VERTEX SET | MATHEMATICS | K-4)-FREE 4-REGULAR GRAPHS | CYCLES | PLANAR GRAPHS | Computer Science | Discrete Mathematics

Min-max theorems | [formula omitted]-completeness | Line graph | Approximation hardness | Independence number | Matching number | NP-completeness | CLAW | RATIO | MATCHINGS | HAMILTONIAN PATH PROBLEM | INDEPENDENT SETS | FEEDBACK VERTEX SET | MATHEMATICS | K-4)-FREE 4-REGULAR GRAPHS | CYCLES | PLANAR GRAPHS | Computer Science | Discrete Mathematics

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2019, Volume 39, Issue 3, pp. 731 - 740

A variant of the Lovász Conjecture on hamiltonian paths states that . Given a finite group and a connection set , the Cayley graph ) will be called if for...

hamiltonian cycle | 05C45 | 05C99 | Cayley graph | normal connection set

hamiltonian cycle | 05C45 | 05C99 | Cayley graph | normal connection set

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2015, Volume 194, pp. 102 - 120

We investigate the set of cycle lengths occurring in bipartite graphs with large minimum degree. A bipartite graph is if it contains cycles of every even...

Minimum degree | Bipartite graph | Hamiltonian cycle | Weakly bipancyclic | MATHEMATICS, APPLIED | HAMILTONIAN GRAPHS | PANCYCLIC GRAPHS | CYCLES

Minimum degree | Bipartite graph | Hamiltonian cycle | Weakly bipancyclic | MATHEMATICS, APPLIED | HAMILTONIAN GRAPHS | PANCYCLIC GRAPHS | CYCLES

Journal Article

Information Processing Letters, ISSN 0020-0190, 11/2015, Volume 115, Issue 11, pp. 877 - 881

Given a set of points in the plane, the of is the geometric graph with vertex set , where are connected by an edge if and only if the closed disk having...

Computational geometry | Gabriel graphs | Hamiltonian cycles | Proximity graphs | DELAUNAY GRAPHS | RELATIVE NEIGHBORHOOD GRAPHS | COMPUTER SCIENCE, INFORMATION SYSTEMS | POINTS

Computational geometry | Gabriel graphs | Hamiltonian cycles | Proximity graphs | DELAUNAY GRAPHS | RELATIVE NEIGHBORHOOD GRAPHS | COMPUTER SCIENCE, INFORMATION SYSTEMS | POINTS

Journal Article

Journal of Intelligent and Fuzzy Systems, ISSN 1064-1246, 2018, Volume 35, Issue 3, pp. 3413 - 3419

Graph theory includes two unavoidable graphs, namely Euler graphs and Hamiltonian graphs. In this study, generalized fuzzy Euler graphs (GFEGs) and generalized...

effective edge | and travelling problems | Euler graphs | Hamiltonian graphs | Generalized fuzzy graphs | travelling problems | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Graphs | Graph theory | Routing (telecommunications) | Fuzzy systems

effective edge | and travelling problems | Euler graphs | Hamiltonian graphs | Generalized fuzzy graphs | travelling problems | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Graphs | Graph theory | Routing (telecommunications) | Fuzzy systems

Journal Article

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