- 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...
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.
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,...
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...
<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...
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.
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.
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.
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...
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...
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
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...
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....
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,...
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.
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...
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