Articles publicats (Matemàtica)
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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 ... 
On Vosperian and Superconnected VertexTransitive Digraphs
(Springer, 2013)We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization ... 
Perfect (super) EdgeMagic Crowns
(Springer, 2017)A graph G is called edgemagic if there is a bijective function f from the set of vertices and edges to the set {1,2, ,V(G)+E(G)} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is ... 
A new labeling construction from the ⊗hproduct
(Elsevier, 2017)The product that is referred in the title was introduced in 2008 as a generalization of the Kronecker product of digraphs. Many relations among labelings have been obtained since then, always using as a second factor a ... 
Distance labelings: a generalization of Langford sequences
(University of Primorska, 2017)A Langford sequence of order m and defect d can be identified with a labeling of the vertices of a path of order 2m in which each label from d up to d + m − 1 appears twice and in which the vertices that have been labeled ... 
Rainbow eulerian multidigraphs and the product of cycles
(DMTCS, 2016)An arc colored eulerian multidigraph with $l$ colors is rainbow eulerian if there is an eulerian circuit in which a sequence of $l$ colors repeats. The digraph product that refers the title was introduced by FigueroaCenteno ... 
On the betanumber of forests with isomorphic components
(De Gruyter Open, 2018)The betanumber, β (G), of a graph G is defined to be either the smallest positive integer n for which there exists an injective function f : V (G) → {0, 1, . . . , n} such that each uv ∈ E (G) is labeled f (u) − f (v) ... 
(Di)graph products, labelings and related results
(Elsevier, 2017)Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can ... 
Langford sequences and a product of digraphs
(Elsevier, 2016)Skolem and Langford sequences and their many generalizations have applications in numerous areas. The product is a generalization of the direct product of digraphs. In this paper we use the product and super edgemagic ... 
Connectivity and other invariants of generalized products of graphs
(Springer, 2015)FigueroaCenteno et al. [4] introduced the following product of digraphs let D be a digraph and let Γ be a family of digraphs such that V (F) = V for every F∈Γ . Consider any function h:E(D)→Γ . Then the product D⊗hΓ is ... 
Sufficient conditions for a digraph to admit a (1,≤ℓ)identifying code
(University of Zielona Góra, 2019)A (1, ≤ `)identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ` have distinct closed inneighbourhoods within C. In this paper, we give some ... 
Repairing an aggregationbased smart metering system
(Springer Berlin Heidelberg, 20190405)Smart meters inform the electricity suppliers about the consumption of their clients in short intervals. Finegrained electricity consumption information is highly sensitive as it has been proven to permit to infer people's ... 
Open problems involving super edgemagic labelings and related topics
(Institute of Combinatorics and its Applications, 2012)Graph labelings has experimented a fast development during the last four decades. Two books dedicated to this topic, a very complete survey on the subject and over 1000 papers in the literature constitute a good proof of ... 
Super edgemagic models
(Springer, 2011)In this paper, we generalize the concept of super edgemagic graph by introducing the new concept of super edgemagic models.