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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 spectra 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 wellknown 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, 2019)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 endvertex 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 reallife complex systems are smallword (large local clustering and small diameter) and scalefree (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 Znproperty for digraphs in order to study this relation ... 
On super edgemagic 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 edgemagic decomposable ... 
The power of digraph products applied to labelings
(Elsevier, 2012)The ⊗hproduct was introduced in 2008 by FigueroaCenteno et al. as a way to construct new families of (super) edgemagic graphs and to prove that some of those families admit an exponential number of (super) edgemagic ... 
Bimagic and other generalizations of super edgemagic labelings
(Cambridge University Press, 2011)In this paper, we use the product ⊗h in order to study super edgemagic labelings, bimagic labelings and optimal kequitable labelings. We establish, with the help of the product ⊗h, new relations between super edgemagic ... 
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 wellknown 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 dregular 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, 20181109)This work provides upper bounds on the cyclicity of the centers on center manifolds in the wellknown 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 matrixbased 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) edgemagic labelings
(2013)A graph G of order p and size q is edgemagic 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 edgemagic labeling of G and the ... 
Enumerating super edgemagic labelings for some types of pathlike 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 edgemagic labelings of some types of pathlike trees. As a ... 
The jumping knight and other (super) edgemagic 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 edgemagic 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 edgemagic labelings of cycles
(Cambridge University Press, 20140614)Kotzig and Rosa defined in 1970 the concept of edgemagic 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 edgemagicness 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 ... 
Large restricted sumsets in general Abelian groups
(Elsevier, 2013)Let A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect to S is defined as A ∧S B = {a + b : a ∈ A, b ∈ B and a − b /∈ S}. Let LS = maxz∈G {(x, y) : x, y ∈ G, x + y = z and x ... 
Small cutsets in arctransitive digraphs of prime degree
(Elsevier, 2013)We give an upper bound for the size of nontrivial sets that have small boundary in a family of arctransitive digraphs. We state the exact size for these sets in case of prime degree. We also give a lower bound for the ...