### Envíos recientes

• #### The spectra of lifted digraphs ﻿

(Springer, 2019-01-02)
We present a method to derive the complete spectrum of the lift Γα of a base digraph Γ , with voltage assignment α on a (finite) group G. The method is based on assigning to Γ a quotient-like matrix whose entries are ...
• #### The spectral excess theorem for graphs with few eigenvalues whose distance- 2 or distance-1-or-2 graph is strongly regular ﻿

(Taylor & Francis, 2018-07-13)
We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and ...
• #### Spectra and eigenspaces of arbitrary lifts of graphs ﻿

(Faculty of Mathematics, Physics and Informatics, Comenius University, 2019)
We describe, in a very explicit way, a method for determining the spec-tra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regularor not).
• #### El mètode de les línies per a la resolució aproximada d'equacions en derivades parcials ﻿

(Societat Catalana de Matemàtiques, Institut d’Estudis Catalans, 2019)
En aquest treball es descriu un mètode numèric semidiscret per a la resolució d'un tipus d'equacions en derivades parcials. És conegut com el mètode de les línies (MOL, per les sigles en anglès), i es basa en la discretització ...
• #### The diameter of cyclic Kautz digraphs ﻿

(Faculty of Sciences and Mathematics, University of Nis, Serbia, 2017)
We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the well-known Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of ...
• #### On the Randić index of graphs ﻿

(Elsevier, 2018-09-11)
For a given graph G = (V, E), the degree mean rate of an edge uv ∈ E is a half of the quotient between the geometric and arithmetic means of its end-vertex degrees d(u) and d(v). In this note, we derive tight bounds for ...
• #### A note on a new general family of deterministic hierarchical networks ﻿

(World Scientific Publishing, 2019)
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. ...
• #### Magic coverings and the Kronecker product ﻿

(2014)
In this paper we study a relationship existing among (super) magic coverings and the well known Kronecker product of matrices. We also introduce the concept of Zn-property for digraphs in order to study this relation ...
• #### On super edge-magic decomposable graphs ﻿

(Springer, 2012)
Let G be any graph and let {Hi}i∈I be a family of graphs such that E(Hi) ∩ E(Hj ) = ∅ when i 6= j, ∪i∈IE(Hi) = E(G) and E(Hi) 6= ∅ for all i ∈ I. In this paper we introduce the concept of {Hi}i∈I -super edge-magic decomposable ...
• #### The power of digraph products applied to labelings ﻿

(Elsevier, 2012)
The ⊗h-product was introduced in 2008 by Figueroa-Centeno et al. as a way to construct new families of (super) edge-magic graphs and to prove that some of those families admit an exponential number of (super) edge-magic ...
• #### Bi-magic and other generalizations of super edge-magic labelings ﻿

(Cambridge University Press, 2011)
In this paper, we use the product ⊗h in order to study super edge-magic labelings, bi-magic labelings and optimal k-equitable labelings. We establish, with the help of the product ⊗h, new relations between super edge-magic ...
• #### Every tree is a large subtree of a tree that decomposes Kn or Kn,n ﻿

(Elsevier, 2010)
Let T be a tree with m edges. A well-known conjecture of Ringel states that every tree T with m edges decomposes the complete graph K2m+1. Graham and H¨aggkvist conjectured that T also decomposes the complete bipartite ...
• #### Vertex‐transitive graphs that remain connected after failure of a vertex and its neighbors ﻿

(Wiley, 2011)
A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex ...
• #### Center cyclicity of Lorenz, Chen and Lü systems ﻿

(Elsevier, 2018-11-09)
This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-known Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from ...
• #### A new approach to gross error detection for GPS networks ﻿

(Elsevier, 2019)
We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, ...
• #### New problems related to the valences of (super) edge-magic labelings ﻿

(2013)
A graph G of order p and size q is edge-magic if there is a bijective function f : V (G) ∪ E(G) −→ {i} p+q i=1 such that f(x) + f(xy) + f(y) = k , for all xy ∈ E(G) . The function f is an edge-magic labeling of G and the ...
• #### Enumerating super edge-magic labelings for some types of path-like trees ﻿

(University of Manitoba, 2015)
The main goal of this paper is to use a variation of the Kronecker product of matrices in order to obtain lower bounds for the number of non isomorphic super edge-magic labelings of some types of pathlike trees. As a ...
• #### The jumping knight and other (super) edge-magic constructions ﻿

(Springer, 2014)
Let G be a graph of order p and size q with loops allowed. A bijective function f:V(G)∪E(G)→{i}p+qi=1 is an edge-magic labeling of G if the sum f(u)+f(uv)+f(v)=k is independent of the choice of the edge uv. The constant k ...
• #### A problem on edge-magic labelings of cycles ﻿

(Cambridge University Press, 2014-06-14)
Kotzig and Rosa defined in 1970 the concept of edge-magic labelings as follows: let G be a simple (p, q)-graph (that is, a graph of order p and size q without loops or multiple edges). A bijective function f : V (G)∪E(G) ...
• #### Labeling constructions using digraph products ﻿

(Elsevier, 2013)
In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super ...