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Arc-disjoint in- and out-branchings rooted at the same vertex in compositions of digraphs

Discrete Mathematics, ISSN 0012-365X, 05/2020, Volume 343, Issue 5, p. 111816

A digraph D=(V,A) has a good pair at a vertex r if D has a pair of arc-disjoint in- and out-branchings rooted at r. Let T be a digraph with t vertices u1,…,ut...

Branching | Semicomplete digraph | Digraph composition

Branching | Semicomplete digraph | Digraph composition

Journal Article

Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 3/2018, Volume 49, Issue 1, pp. 113 - 127

Let $$\vec G$$ G → be a strongly connected digraph and Q( $$\vec G$$ G → ) be the signless Laplacian matrix of $$\vec G$$ G → . The spectral radius of Q(...

{\tilde \infty _1}$$ ∞ ˜ 1 -digraph | {\tilde \theta _2}$$ θ ˜ 2 -digraph | {\tilde \infty _2}$$ ∞ ˜ 2 -digraph | Numerical Analysis | Mathematics, general | Mathematics | Applications of Mathematics | The signless Laplacian spectral radius | {\tilde \theta _1}$$ θ ˜ 1 -digraph | digraph | MATHEMATICS | TREES | he signless Laplacian spectral radius | (infinity)over-tilde-digraph | (theta)over-tilde-digraph | GRAPHS | Analysis | Graph theory

{\tilde \infty _1}$$ ∞ ˜ 1 -digraph | {\tilde \theta _2}$$ θ ˜ 2 -digraph | {\tilde \infty _2}$$ ∞ ˜ 2 -digraph | Numerical Analysis | Mathematics, general | Mathematics | Applications of Mathematics | The signless Laplacian spectral radius | {\tilde \theta _1}$$ θ ˜ 1 -digraph | digraph | MATHEMATICS | TREES | he signless Laplacian spectral radius | (infinity)over-tilde-digraph | (theta)over-tilde-digraph | GRAPHS | Analysis | Graph theory

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2018, Volume 238, pp. 161 - 166

A digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length ≤k from u to v is called a k-geodetic...

Moore bound | Excess one digraph | Diregularity | Characteristic polynomial | [formula omitted]-geodetic digraph | k-geodetic digraph | MATHEMATICS, APPLIED | kappa-geodetic digraph | MOORE DIGRAPHS

Moore bound | Excess one digraph | Diregularity | Characteristic polynomial | [formula omitted]-geodetic digraph | k-geodetic digraph | MATHEMATICS, APPLIED | kappa-geodetic digraph | MOORE DIGRAPHS

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 06/2017, Volume 85, Issue 2, pp. 545 - 567

The k‐linkage problem is as follows: given a digraph D=(V,A) and a collection of k terminal pairs (s1,t1),…,(sk,tk) such that all these vertices are distinct;...

polynomial algorithm | disjoint paths | k‐linkage problem | quasi‐transitive digraph | (round‐)decomposable digraphs | locally semicomplete digraph | (round-)decomposable digraphs | k-linkage problem | quasi-transitive digraph | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS | TOURNAMENTS | LOCALLY SEMICOMPLETE DIGRAPHS

polynomial algorithm | disjoint paths | k‐linkage problem | quasi‐transitive digraph | (round‐)decomposable digraphs | locally semicomplete digraph | (round-)decomposable digraphs | k-linkage problem | quasi-transitive digraph | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS | TOURNAMENTS | LOCALLY SEMICOMPLETE DIGRAPHS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 05/2013, Volume 33, Issue 2, pp. 247 - 260

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices...

4-transitive digraph | k-quasi-transitive digraph | k-transitive digraph | digraph | transitive digraph | quasi-transitive digraph | K-transitive digraph | Transitive digraph | Quasi-transitive digraph | Digraph | K-quasi-transitive digraph | MATHEMATICS | quasi-transitive digraph,4-transitive digraph

4-transitive digraph | k-quasi-transitive digraph | k-transitive digraph | digraph | transitive digraph | quasi-transitive digraph | K-transitive digraph | Transitive digraph | Quasi-transitive digraph | Digraph | K-quasi-transitive digraph | MATHEMATICS | quasi-transitive digraph,4-transitive digraph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2019, Volume 342, Issue 2, pp. 473 - 486

According to Richardson’s theorem, every digraph G without directed odd cycles that is either (a) locally finite or (b) rayless has a kernel (an independent...

Digraph kernel | End of a digraph | Infinite digraph | MATHEMATICS | DIRECTED-GRAPHS

Digraph kernel | End of a digraph | Infinite digraph | MATHEMATICS | DIRECTED-GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 11/2013, Volume 313, Issue 22, pp. 2582 - 2591

Let D=(V(D),A(D)) be a digraph and k≥2 an integer. We say that D is k-quasi-transitive if for every directed path (v0,v1,…,vk) in D we have (v0,vk)∈A(D) or...

Quasi-transitive digraph | Digraph | [formula omitted]-quasi-transitive digraph | [formula omitted]-king | Digraph k-king | k-quasi-transitive digraph | MATHEMATICS | 4-KINGS | 3-KINGS | k-king | KINGS

Quasi-transitive digraph | Digraph | [formula omitted]-quasi-transitive digraph | [formula omitted]-king | Digraph k-king | k-quasi-transitive digraph | MATHEMATICS | 4-KINGS | 3-KINGS | k-king | KINGS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 609 - 617

We introduce new versions of chordal and split digraphs, and explore their similarity with the corresponding undirected notions.

Split digraph | Chordal digraph | Perfect digraph | Recognition algorithm | MATHEMATICS, APPLIED | RECOGNIZING INTERVAL-GRAPHS | RECOGNITION | ACYCLIC DIGRAPHS | TIME | ALGORITHMS

Split digraph | Chordal digraph | Perfect digraph | Recognition algorithm | MATHEMATICS, APPLIED | RECOGNIZING INTERVAL-GRAPHS | RECOGNITION | ACYCLIC DIGRAPHS | TIME | ALGORITHMS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 223, pp. 1 - 14

In this paper, we study the spectra of weighted digraphs, where weights are taken from the set of non zero real numbers. We obtain formulae for the...

Coulson’s integral formula | Energy of a weighted digraph | Extremal energy | Spectrum of a weighted digraph | Bipartite weighted digraph | McClelland inequality | Coulson's integral formula | SIGNED DIGRAPHS | MATHEMATICS, APPLIED | GRAPHS

Coulson’s integral formula | Energy of a weighted digraph | Extremal energy | Spectrum of a weighted digraph | Bipartite weighted digraph | McClelland inequality | Coulson's integral formula | SIGNED DIGRAPHS | MATHEMATICS, APPLIED | GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2020, Volume 343, Issue 4, p. 111784

Divisible design digraphs which can be obtained as Cayley digraphs are studied. A characterization of divisible design Cayley digraphs in terms of the...

Regular group action | Digraph | Divisible design | Cayley digraph

Regular group action | Digraph | Divisible design | Cayley digraph

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 07/2019, Volume 137, pp. 118 - 125

Given integers k and m, we construct a G-arc-transitive graph of valency k and an L-arc-transitive oriented digraph of out-valency k such that G and L both...

Cayley digraphs | Imprimitive digraphs | Arc-transitive digraphs | MATHEMATICS | Imprirnitive digraphs | THEOREM

Cayley digraphs | Imprimitive digraphs | Arc-transitive digraphs | MATHEMATICS | Imprirnitive digraphs | THEOREM

Journal Article

Advances in Intelligent Systems and Computing, ISSN 2194-5357, 2016, Volume 440, pp. 329 - 339

Conference Proceeding

Discrete Mathematics, ISSN 0012-365X, 10/2018, Volume 341, Issue 10, pp. 2883 - 2893

The concepts of a splicing machine and of an aparalled digraph are introduced. A splicing machine is basically a means to uniquely obtain all circular...

Splicing | Digraph | MATHEMATICS | DNA

Splicing | Digraph | MATHEMATICS | DNA

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 06/2017, Volume 303, pp. 24 - 33

The energy of an n-vertex digraph D is defined by E(D)=∑k=1n|Re(zk)|, where z1,…,zn are eigenvalues of D and Re(zk) is the real part of eigenvalue zk. Very...

Iota energy of digraphs | Bicyclic digraphs | Energy of digraphs | SIGNED DIGRAPHS | MAXIMAL ENERGY | MATHEMATICS, APPLIED | MATCHING ENERGY | LAPLACIAN-ENERGY | GRAPHS

Iota energy of digraphs | Bicyclic digraphs | Energy of digraphs | SIGNED DIGRAPHS | MAXIMAL ENERGY | MATHEMATICS, APPLIED | MATCHING ENERGY | LAPLACIAN-ENERGY | GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2019, Volume 342, Issue 4, pp. 1128 - 1138

In this paper, based on the calculation using GAP, we give a classification result on arc-transitive Cayley digraphs of finite simple groups. Let G be a finite...

Simple group | Cayley digraph | Alternatingly connected digraph | Arc-transitive digraph | PRIMITIVE PERMUTATION-GROUPS | MATHEMATICS | AUTOMORPHISM-GROUPS | DEGREE LESS | GRAPHS

Simple group | Cayley digraph | Alternatingly connected digraph | Arc-transitive digraph | PRIMITIVE PERMUTATION-GROUPS | MATHEMATICS | AUTOMORPHISM-GROUPS | DEGREE LESS | GRAPHS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2012, Volume 436, Issue 7, pp. 2524 - 2530

Let D be a digraph with vertex set V(D) and A be the adjacency matrix of D. In this paper, we characterize the extremal digraphs which achieve the maximum and...

Bicyclic digraph | θ-Digraph | Digraph | Spectral radius | MATHEMATICS | MATHEMATICS, APPLIED | theta-Digraph | infinity-Digraph

Bicyclic digraph | θ-Digraph | Digraph | Spectral radius | MATHEMATICS | MATHEMATICS, APPLIED | theta-Digraph | infinity-Digraph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2020, Volume 343, Issue 5, p. 111827

Let P2,2 be the orientation of C4 which consists of two 2-paths with the same initial and terminal vertices. In this paper, we determine the maximum size of...

Path | Turán problem | Digraph | Cycle

Path | Turán problem | Digraph | Cycle

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2020, Volume 343, Issue 5, p. 111794

In 1996, Bang-Jensen, Gutin, and Li proposed the following conjecture: If D is a strong digraph of order n where n≥2 with the property that d(x)+d(y)≥2n−1 for...

Hamiltonian cycle | Digraph | Degree condition

Hamiltonian cycle | Digraph | Degree condition

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2019, Volume 269, pp. 68 - 76

We present some applications of a new matrix approach for studying the properties of the lift Γα of a voltage digraph, which has arcs weighted by the elements...

Abelian group | Voltage digraphs | Quotient digraph | Lifted digraph | Adjacency matrix | Regular partition | Digraph | Generalized Petersen graph | Spectrum | MATHEMATICS, APPLIED | Completeness | Graph theory | Directed graphs | Matemàtica discreta | Grafs, Teoria de | spectrum | Teoria de grafs | Matemàtiques i estadística | Àrees temàtiques de la UPC

Abelian group | Voltage digraphs | Quotient digraph | Lifted digraph | Adjacency matrix | Regular partition | Digraph | Generalized Petersen graph | Spectrum | MATHEMATICS, APPLIED | Completeness | Graph theory | Directed graphs | Matemàtica discreta | Grafs, Teoria de | spectrum | Teoria de grafs | Matemàtiques i estadística | Àrees temàtiques de la UPC

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2019, Volume 35, Issue 3, pp. 669 - 675

Kernel is an important topic in digraphs. A digraph such that every proper induced subdigraph has a kernel is said to be critical kernel imperfect (CKI, for...

Arc-locally in-semicomplete digraph | 05C20 | Generalization of bipartite tournaments | CKI-digraph | Mathematics | Engineering Design | Combinatorics | 3-Anti-quasi-transitive digraph | 05C69 | Kernel | 3-Quasi-transitive digraph | MATHEMATICS | Kernels | Asymmetry | Graph theory

Arc-locally in-semicomplete digraph | 05C20 | Generalization of bipartite tournaments | CKI-digraph | Mathematics | Engineering Design | Combinatorics | 3-Anti-quasi-transitive digraph | 05C69 | Kernel | 3-Quasi-transitive digraph | MATHEMATICS | Kernels | Asymmetry | Graph theory

Journal Article

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