Abel Cabrera Martínez

ORCID: 0000-0003-2806-4842
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Research Areas
  • Advanced Graph Theory Research
  • Complexity and Algorithms in Graphs
  • Graph Labeling and Dimension Problems
  • Graph theory and applications
  • Limits and Structures in Graph Theory
  • Interconnection Networks and Systems
  • Corneal surgery and disorders
  • Optimization and Search Problems
  • Ocular Infections and Treatments
  • Cooperative Communication and Network Coding
  • Peroxisome Proliferator-Activated Receptors
  • Retinal Diseases and Treatments
  • Retinal Imaging and Analysis
  • Aging, Health, and Disability
  • Game Theory and Voting Systems
  • Higher Education Teaching and Evaluation
  • Glaucoma and retinal disorders
  • Developmental and Educational Neuropsychology
  • Nuclear Receptors and Signaling
  • Architecture and Art History Studies
  • Organizational Management and Innovation
  • Quality of Life Measurement
  • melanin and skin pigmentation
  • Dye analysis and toxicity
  • Data Visualization and Analytics

University of Córdoba
2022-2024

Universitat Rovira i Virgili
2018-2024

University of Maribor
2022

Universidad de Cádiz
2018-2019

Consejería de Educación y Empleo
2018

Universidad Autónoma de Guerrero
2016-2018

Hospital Oncológico Docente "Conrado Benítez García"
2007-2009

Instituto Cubano de Oftalmología "Ramón Pando Ferrer"
2007-2009

Ferrer Grupo (Spain)
2007

A set $D$ of vertices a graph $G$ is total dominating if every vertex adjacent to at least one in $D$. The called co-independent $V(G)\setminus D$ an independent and has vertex. minimum cardinality any denoted by $\gamma_{t,coi}(G)$. In this paper, we show that, for tree $T$ order $n$ diameter three, $n-\beta(T)\leq \gamma_{t,coi}(T)\leq n-|L(T)|$ where $\beta(T)$ the maximum $L(T)$ leaves $T$. We also characterize families trees attaining extremal bounds above that differences between value...

10.55016/ojs/cdm.v19i3.75096 article EN Contributions to Discrete Mathematics 2024-09-23

10.1016/j.dam.2022.03.022 article EN Discrete Applied Mathematics 2022-04-08

A subset D of vertices a graph G is total dominating set if every vertex adjacent to at least one D. The called co-independent the subgraph induced by V−D edgeless and has vertex. minimum cardinality any domination number denoted γt,coi(G)⁠. In this work we study some complexity combinatorial properties Specifically, prove that deciding whether γt,coi(G)≤k for given integer k an NP-complete problem give several bounds on Moreover, since set, characterize all trees having equal number.

10.1093/comjnl/bxy038 article EN The Computer Journal 2018-04-04

10.1016/j.dam.2018.05.025 article EN publisher-specific-oa Discrete Applied Mathematics 2018-08-16

10.1016/j.dam.2018.12.018 article EN publisher-specific-oa Discrete Applied Mathematics 2019-01-11

Given a graph G = ( V , E ) function f : → { 0 1 2 ⋯ } is said to be total dominating if ∑ u ∈ N v > for every where denotes the open neighbourhood of v. Let i x . We say that weak Roman and vertex there exists ∩ ∪ such ′ defined by − whenever \ as well. The weight w In this article, we introduce study domination number G, denoted γ t r which minimum among all functions on G. show close relationship between novel parameter other parameters graph. Furthermore, obtain general bounds and,...

10.3390/sym11060831 article EN Symmetry 2019-06-24

Let G be a graph without isolated vertices. A function f : V ( ) → { 0 , 1 2 } is total Roman dominating on if every vertex v ∈ for which = adjacent to at least one u such that and the subgraph induced by set ≥ has no The domination number of G, denoted γ t R minimum weight ω ∑ among all functions G. In this article we obtain new tight lower upper bounds improve well-known ≤ 3 where represents classical number. addition, characterize graphs achieve equality in previous bound give necessary...

10.3390/math8030349 article EN cc-by Mathematics 2020-03-05

10.1016/j.dam.2021.05.011 article EN Discrete Applied Mathematics 2021-05-25

<abstract><p>Let $ G be a nontrivial graph and k\geq 1 an integer. Given vector of nonnegative integers w = (w_0, \ldots, w_k) $, function f: V(G)\rightarrow \{0, k\} is $-dominating on if f(N(v))\geq w_i for every v\in V(G) such that f(v) i $. The $-domination number denoted by \gamma_{w}(G) the minimum weight \omega(f) \sum_{v\in V(G)}f(v) among all functions In particular, \{2\} defined as \gamma_{\{2\}}(G) \gamma_{(2, 1, 0)}(G) this paper we continue with study graphs. obtain...

10.3934/math.2022599 article EN cc-by AIMS Mathematics 2022-01-01

A set D of vertices a graph G is total dominating if every vertex adjacent to at least one D. The called co-independent the subgraph induced by V (G) -D edgeless.The minimum cardinality among all sets domination number G.In this article we study join, strong, lexicographic, direct and rooted products graphs.

10.33044/revuma.1652 article EN cc-by Revista de la Unión Matemática Argentina 2022-05-17

A total dominating set D of a graph G is said to be secure if for every vertex u ∈ V ( ) \ , there exists v which adjacent u, such that { } ∪ as well. The domination number the minimum cardinality among all sets G. In this article, we obtain new relationships between and other parameters: namely independence number, matching parameters. Some our results are tight bounds improve some well-known results.

10.3390/sym11091165 article EN Symmetry 2019-09-15

A set D of vertices a graph G is double dominating if |N[v]∩D|≥2 for every v∈V(G), where N[v] represents the closed neighbourhood v. The domination number minimum cardinality among all sets G. In this article, we show that and H are graphs with no isolated vertex, then any vertex v∈V(H) there six possible expressions, in terms parameters factor graphs, rooted product G∘vH. Additionally, characterize satisfy each these expressions.

10.1016/j.dam.2023.06.021 article EN cc-by-nc-nd Discrete Applied Mathematics 2023-06-26

Given a graph $G=(V,E)$, function $f:V\rightarrow \{0,1,2\}$ is total Roman $\{2\}$-dominating if: (1) every vertex $v\in V$ for which $f(v)=0$ satisfies that $\sum_{u\in N(v)}f(u)\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and (2) $x\in $f(x)\geq 1$ adjacent to at least one $y\in such $f(y)\geq 1$. The weight $f$ defined as $\omega(f)=\sum_{v\in V}f(v)$. $\{2\}$-domination number, denoted by $\gamma_{t\{R2\}}(G)$, minimum among all functions on $G$. In this article we...

10.2989/16073606.2019.1695230 article EN Quaestiones Mathematicae 2019-11-28

Let G be a graph of order n(G) and vertex set V(G). Given S ⊆ V(G), we define the perfect neighbourhood as Np(S) all vertices in V(G)\S having exactly one neighbour S. The differential is defined to ∂p(S) = |Np(S)| − |S|. In this paper, introduce study graph, which ∂p(G) max{∂p(S) : V(G)}. Among other results, obtain general bounds on prove Gallai-type theorem, states that + γpR(G) n(G), where denotes Roman domination number G. As consequence study, show some classes graphs satisfying...

10.2989/16073606.2020.1858992 article EN Quaestiones Mathematicae 2021-01-19

Let G be a graph with no isolated vertex and f : V ( ) → {0, 1, 2} function. i = { x ∈ } for every . We say that is total Roman dominating function on if in 0 adjacent to at least one 2 the subgraph induced by 1 ∪ has vertex. The weight of ω ∑ v minimum among all functions domination number , denoted γ t R It known general problem computing NP-hard. In this paper, we show H nontrivial graph, then lexicographic product ∘ given ≥ 2, ξ where parameter defined

10.26493/1855-3974.2284.aeb article EN Ars Mathematica Contemporanea 2021-03-11

In this paper, we show that the Italian domination number of every lexicographic product graph G ○ H can be expressed in terms five different parameters . These defined under following unified approach, which encompasses definition several well-known and introduces new ones. Let N ( v ) denote open neighbourhood ∈ V , let w = 0 1 …, l a vector nonnegative integers such ≥ We say function f : → {0, 1, } is -dominating if )) ∑ u i for vertex with The weight to ω -domination denoted by γ minimum...

10.26493/1855-3974.2318.fb9 article EN Ars Mathematica Contemporanea 2021-05-12

10.7151/dmgt.2318 article EN cc-by-nc-nd Discussiones Mathematicae Graph Theory 2020-01-01

Given a graph G without isolated vertices, total Roman dominating function for is f:V(G)→{0,1,2} such that every vertex u with f(u)=0 adjacent to v f(v)=2, and the set of vertices positive labels induces minimum degree at least one. The domination number γtR(G) smallest possible value ∑v∈V(G)f(v) among all functions f. direct product G×H graphs H studied in this work. Specifically, several relationships, shape upper lower bounds, between γtR(G×H) some classical parameters factors are given....

10.3390/math8091438 article EN cc-by Mathematics 2020-08-27

A set of vertices a graph G is total dominating if every vertex adjacent to at least one in such set. We say that D outer k-independent the maximum degree subgraph induced by are not less or equal k − 1 . The minimum cardinality among all sets domination number G. In this article, we introduce parameter and begin with study its combinatorial computational properties. For instance, give several closed relationships between novel other ones related independence graphs. addition,...

10.3390/math8020194 article EN cc-by Mathematics 2020-02-05

10.1016/j.dam.2020.03.058 article EN publisher-specific-oa Discrete Applied Mathematics 2020-04-08

Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} function. If f satisfies that every in the set {v∈V(G):f(v)=0} is adjacent to at least one {v∈V(G):f(v)=2}, if subgraph induced by {v∈V(G):f(v)≥1} has vertex, then we say total Roman dominating function on G. The minimum weight ω(f)=∑v∈V(G)f(v) among all functions domination number of In this article study parameter for rooted product graphs. Specifically, obtain closed formulas tight bounds graphs terms invariants factor involved product.

10.3390/math8101850 article EN cc-by Mathematics 2020-10-20

Abstract Let G be a graph of minimum degree at least two. A set $$D\subseteq V(G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>⊆</mml:mo> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is said to double total dominating if $$|N(v)\cap D|\ge 2$$ <mml:mo>|</mml:mo> <mml:mi>N</mml:mi> <mml:mi>v</mml:mi> <mml:mo>∩</mml:mo> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> for every vertex $$v\in...

10.1007/s40840-021-01200-0 article EN cc-by Bulletin of the Malaysian Mathematical Sciences Society 2021-10-05

A Roman dominating function on a graph G = (V (G), E(G)) is f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which (u) 0 adjacent to at least one v (v) 2.The an outer-independent if set of vertices labeled with zero under independent set.The domination number γ oiR minimum weight w(f ) v∈V any G.A cover covers all edges G.The cardinality denoted by α(G).A

10.7151/dmgt.2179 article EN cc-by-nc-nd Discussiones Mathematicae Graph Theory 2018-11-21
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