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Linear Algebra and Its Applications, ISSN 0024-3795, 07/2016, Volume 500, pp. 1 - 14
Denote the scrambling index set of primitive minimally strong digraphs of order n by SIn. For n≥13, we show that SIn contains all integers in the interval... 
Scrambling index | Index set | Primitive digraph
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 2016, Volume 16, Issue 9
We attach a diagraph with generalized Quaternion group of order 4n by utilizing the power map f : Q(4n) -> Q(4n) defined by f(x) = x(k) for all x is an element... 
Generalized quaternion group | semi-regular digraph | fixed point | cycles | in-degree | iteration digraph | regular digraph | MATHEMATICS | MATHEMATICS, APPLIED | MODULO N
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 07/2017, Volume 687, pp. 1 - 10
The Kautz graphs are a famous class of network models and the super-λ property of graphs is a good indicator of the fault tolerance of networks. We, in this... 
Kautz digraph | Fault tolerance | Connectivity | Digraph | Network | RESTRICTED EDGE-CONNECTIVITY | NETWORKS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 11/2017, Volume 127, pp. 1 - 13
We solve the long-standing existence problem of vertex-primitive 2-arc-transitive digraphs by constructing an infinite family of such digraphs. 
Vertex-primitive | 2-arc-transitive | Digraphs | MATHEMATICS | ARC-TRANSITIVE DIGRAPHS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2016, Volume 496, pp. 71 - 80
The comparisons of the Brualdi-type eigenvalue inclusion set provided by Bu et al. (2015) [3] and the Brauer-type eigenvalue inclusion set provided by Li and... 
Eigenvalue | Tensor | Digraph | Brualdi | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2015, Volume 338, Issue 8, pp. 1501 - 1508
In a digraph G=(V,A), a vertex u is said to dominate its out-neighbors v, that is, there is an arc (u,v)∈A. A set D⊆V is a dominating set of G if each vertex... 
Generalized de Bruijn digraph | Combinatorial problems | Efficient domination | Dominating set | Digraph | MATHEMATICS | NUMBERS | TWIN DOMINATION
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 03/2014, Volume 526, pp. 28 - 40
We consider the problem of deciding whether a given network with integer capacities has two feasible flows x and y with prescribed balance vectors such that... 
Linkages | Spanning connected Eulerian digraph | Even cycle factor | Acyclic digraph | Odd cycle factor | Arc-disjoint flows | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Algorithms | Computer Science | Discrete Mathematics
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 09/2018, Volume 89, Issue 1, pp. 64 - 75
A digraph D is supereulerian if D has a spanning closed ditrail. Bang‐Jensen and Thomassé conjectured that if the arc‐strong connectivity λ(D) of a digraph D... 
independence number | arc‐strong connectivity | eulerian digraph | matching number | supereulerian bipartite digraph | arc-strong connectivity | MATHEMATICS | CYCLES | GRAPHS
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 11/2015, Volume 49, pp. 323 - 330
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a... 
partial line digraphs | diameter | line digraphs | Kautz digraphs | Partial line digraphs | Line digraphs | Diameter | Grafs, Teoria de | Directed graphs | Matemàtiques i estadística | Graph theory | Àrees temàtiques de la UPC
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 07/2013, Volume 439, Issue 1, pp. 106 - 132
Let D be a directed graph without loops or multiple arcs, with vertex set V(D)=V and arc set E(D)=E. Let D0 be the digraph with vertex set V and with no arcs,... 
Adjacency polynomial | xyz-Transformation | Digraph-function | Regular digraph | Cospectral digraphs | GRAPH | MATHEMATICS, APPLIED | NUMBER | CHARACTERISTIC-POLYNOMIALS | SPANNING-TREES | COVERINGS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 3/2016, Volume 32, Issue 2, pp. 629 - 638
Let H be a digraph possibly with loops and D a finite digraph without loops whose arcs are coloured with the vertices of H (D is an H-coloured digraph). The... 
Color-class digraph | 05C20 | H -coloured digraph | Mathematics | Kernel by monochromatic paths | H -kernel | Engineering Design | Combinatorics | 05C69 | Kernel | 05C38 | H-kernel | H-coloured digraph
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2015, Volume 65, Issue 4, pp. 923 - 945
For any two positive integers n and k ⩾ 2, let G(n, k) be a digraph whose set of vertices is {0, 1, …, n − 1} and such that there is a directed edge from a... 
05C20 | 11A07 | tree | Mathematics | 11A15 | congruence | digraph product | Ordinary Differential Equations | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematical Modeling and Industrial Mathematics | fundamental constituent | symmetric digraph | 68R10 | 05C05 | semiregular digraph | CONGRUENCE X(K) | MATHEMATICS | SYMMETRIC DIGRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2017, Volume 233, pp. 83 - 93
Hefner et al. (1991) characterized acyclic digraphs each vertex of which has indegree and outdegree at most two and whose competition graphs are interval. They... 
Chordal graph | Moral graph | Phylogeny graph | Competition graph | [formula omitted] digraph | (2,2) digraph | MATHEMATICS, APPLIED | NUMBERS | TOURNAMENT | BELIEF NETWORKS | (1,2)-STEP COMPETITION GRAPH | PROBABILISTIC INFERENCE | Phylogeny | Employee motivation
Journal Article
Physics Reports, ISSN 0370-1573, 12/2013, Volume 533, Issue 4, pp. 95 - 142
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the... 
Graph clustering | Community detection | Directed networks | Complex networks | Graph mining | INTERNET | PHYSICS, MULTIDISCIPLINARY | MODULARITY | PATTERNS | IDENTIFICATION | DIGRAPH LAPLACIAN | MODELS | RANDOM-WALKS | Computer science | Surveys | Algorithms
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 09/2019, Volume 577, pp. 21 - 40
Let M be a partitioned matrix and B be its equitable quotient matrix. In this paper, we prove the inclusion of their spectra σ(B)⊆σ(M), and the equality of... 
Quotient matrix | Matrix | Graph | Digraph | Spectral radius | Spectrum | MATHEMATICS, APPLIED | ENERGY | DIGRAPHS | SIGNLESS LAPLACIAN | GRAPHS | MATHEMATICS | RADIUS | Graphs | Spectra | Graph theory | Quotients
Journal Article
Networks, ISSN 0028-3045, 01/2013, Volume 61, Issue 1, pp. 20 - 28
For a strongly connected digraph D the restricted arc‐connectivity λ′(D) is defined as the minimum cardinality of an arc‐cut over all arc‐cuts S satisfying... 
arc‐cut | line digraph | restricted arc‐connectivity | diameter | s ‐geodetic digraph | restricted arc-connectivity | s -geodetic digraph | arc-cut | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | SUFFICIENT CONDITIONS | CONDITIONAL EDGE-CONNECTIVITY | GIRTH | GRAPHS | s-geodetic digraph | ORDER | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EXTRACONNECTIVITY | Studies | Connectivity
Journal Article
Discrete Mathematics, ISSN 0012-365X, 05/2015, Volume 338, Issue 5, pp. 688 - 694
Let G be a digraph and LG be its line digraph. Levine gave a formula that relates the number of rooted spanning trees of LG and that of G, with the restriction... 
Line digraphs | Weighted digraphs | Out-regular digraphs | Spanning trees | MATHEMATICS | Constrictions | Mathematical analysis | Graph theory
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 08/2017, Volume 61, pp. 577 - 583
The chromatic number of a digraph D is the minimum number of acyclic subgraphs covering the vertex set of D. A tournament H is a hero if every H-free... 
chromatic number of digraphs | Erdős–Hajnal conjecture | Digraph coloring
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 17, pp. 7481 - 7497
This paper studies the link between isomorphic digraphs and isomorphic Leibniz algebras, determining in detail this fact when using (psuedo)digraphs of 2 and 3... 
Leibniz algebra | combinatorial structure | isomorphism class | (pseudo)digraph | algorithm | MATHEMATICS, APPLIED | COMBINATORIAL STRUCTURES | CLASSIFICATION | (pseudo) digraph | Algebra | Isomorphism | Graph theory | Apexes | Combinatorial analysis
Journal Article
Discrete Mathematics, ISSN 0012-365X, 11/2018, Volume 341, Issue 11, pp. 3237 - 3240
The main results provide sufficient conditions for balanced bipartite digraphs to be bipancyclic. These are analogues to well-known results on pancyclic... 
Bipancyclic | Bipartite digraph | Hamiltonian | Balanced | Pancyclic | MATHEMATICS | GRAPHS
Journal Article
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