Papers by Juan Carlos Valenzuela Tripodoro
![Research paper thumbnail of Further Results on the [k]-Roman Domination in Graphs](https://attachments.academia-assets.com/117470677/thumbnails/1.jpg)
Būlitan-i anjuman-i riyāz̤ī-i Īrān., Mar 27, 2024
In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. So... more In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]-Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple version of this Roman-dominationtype problem. Given any labeling of the vertices of a graph, AN (v) stands for the set of neighbors of a vertex v having a positive label. In this paper we continue the study of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the previous versions when 2 ≤ k ≤ 4. Namely, f is a [k]-RDF if f (N [v]) ≥ k +|AN (v)| for all v. We prove that the associate decision problem is NP-complete even when restricted to star convex and comb convex bipartite graphs and we also give sharp bounds and exact values for several classes of graphs.
Maximal double Roman domination in graphs
Applied Mathematics and Computation, Feb 1, 2022
Mixed Roman Domination in Graphs
Bulletin of the Malaysian Mathematical Sciences Society, Jun 4, 2015
Let $$G = (V, E)$$G=(V,E) be a simple graph with vertex set V and edge set E. A mixed Roman domin... more Let $$G = (V, E)$$G=(V,E) be a simple graph with vertex set V and edge set E. A mixed Roman dominating function (MRDF) of G is a function $$f: V\cup E\rightarrow \{0,1,2\}$$f:V∪E→{0,1,2} satisfying the condition every element $$x\in V\cup E$$x∈V∪E for which $$f(x)= 0$$f(x)=0 is adjacent or incident to at least one element $$y\in V\cup E$$y∈V∪E for which $$f(y) = 2$$f(y)=2. The weight of a MRDF f is $$\omega (f)=\sum _{x\in V\cup E}f(x)$$ω(f)=∑x∈V∪Ef(x). The mixed Roman domination number of G is the minimum weight of a mixed Roman dominating function of G. In this paper, we initiate the study of the mixed Roman domination number and we present bounds for this parameter. We characterize the graphs attaining an upper bound and the graphs having small mixed Roman domination numbers.
On the Outer Independent Total Double Roman Domination in Graphs
Mediterranean Journal of Mathematics, Mar 24, 2023
Maximal double Roman domination in graphs
Applied Mathematics and Computation, 2022
Applicable Analysis and Discrete Mathematics, 2015
Maximal connectivity and superconnectivity in a network are two important features of its reliabi... more Maximal connectivity and superconnectivity in a network are two important features of its reliability. In this paper, using graph terminology, we first give a lower bound for the vertex connectivity of the strong product of two networks and then we prove that the resulting structure is more reliable than its generators. Namely, sufficient conditions for a strong product of two networks to be maximally connected and superconnected are given
Applied Mathematics and Computation
We continue the study of restrained double Roman domination in graphs. For a graph G = V (G), E(G... more We continue the study of restrained double Roman domination in graphs. For a graph G = V (G), E(G) , a double Roman dominating function f is called a restrained double Roman dominating function (RDRD function) if the subgraph induced by {v ∈ V (G) | f (v) = 0} has no isolated vertices. The restrained double Roman domination number (RDRD number) γ rdR (G) is the minimum weight v∈V (G) f (v) taken over all RDRD functions of G. We first prove that the problem of computing γ rdR is NP-hard even for planar graphs, and investigate its relationships with some well-known parameters such as restrained domination number γ r and domination number γ by bounding γ rdR from below and above involving γ r and γ for general graphs, respectively. We prove that γ rdR (T) ≥ n + 2 for any tree T = K 1,n−1 of order n ≥ 2 and characterize the family of all trees attaining the lower bound. The characterization of graphs with small RDRD numbers is given in this paper.
Máximo número de aristas de un grafo bipartito sin subgrafos bipartitos completos
V Jornadas De Matematica Discreta Y Algoritmica 2006 Isbn 978 84 8448 380 9 Pags 87 94, 2006
Resultados sobre la vértice-conectividad de un producto de grafos
V Jornadas De Matematica Discreta Y Algoritmica 2006 Isbn 978 84 8448 380 9 Pags 103 110, 2006
Geometría fractal con DERIVE. Tratamiento de imágenes
Epsilon Revista De La Sociedad Andaluza De Educacion Matematica Thales, 2001
Avances en matemática discreta en Andalucía: V Encuentro Andaluz de Matemática Discreta, La Línea de la Concepción (Cádiz), julio de 2007
... Técnica incremental para el cálculo homológico en complejos simpliciales. Rocío González Díaz... more ... Técnica incremental para el cálculo homológico en complejos simpliciales. Rocío González Díaz, María José Jiménez Rodríguez, Belén Medrano Garfia, Pedro Real Jurado. págs. ... Justo Puerto Albandoz, Antonio Manuel Rodríguez Chía, A. Tamir, Dionisio Pérez Brito. págs. ...
Sobre el orden de jaulas bi-regulares
El problema de Turán sobre grafos bipartitos completos
Máximas aristas de un grafo sin subgrafos menores completos
Cotas sobre el orden de las (r, m; g)-jaulas
Grafos bipartitos extremales con cintura dada
Triple Roman domination in graphs
Applied Mathematics and Computation
Discrete Applied Mathematics, 2017
Based on the history that the Emperor Constantine decreed that any undefended place (with no legi... more Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph G = (V, E), is a function f : V → {0, 1, 2} such that every vertex v with f (v) = 0 has at least a neighbor w in G for which f (w) = 2. The Roman domination number of a graph is the minimum weight, v∈V f (v), of a Roman dominating function. In this paper we initiate the study of a new parameter related to Roman domination, which we call strong Roman domination number and denote it by γ StR (G). We approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. In particular, we first show that the decision problem regarding the computation of the strong Roman domination number is NP-complete, even when restricted to bipartite graphs. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, we prove that for any tree T of order n ≥ 3, γ StR (T) ≤ 6n/7 and characterize all extremal trees.
Discussiones Mathematicae Graph Theory
A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for ... more A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f (v) = 0 there is a neighbor u of v with f (u) = 2, or there are two neighbors x, y of v with f (x) = f (y) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F f such that the set of vertices with f (v) > 0 induce a subgraph with no isolated vertices. The weight of a TR2DF is the sum of its function values over all vertices, and the minimum weight of a TR2DF of G is the total Roman {2}-domination number γ tR2 (G). In this paper, we initiate the study of total Roman {2}-dominating functions, where properties are established. Moreover, we present various bounds on the total Roman {2}-domination number. We also show that the decision problem associated with γ tR2 (G) is NP-complete for bipartite and chordal graphs. Moreover, we show that it is 2 H. Abdollahzadeh Ahangar et al. possible to compute this parameter in linear time for bounded clique-width graphs (including trees).
10th Andalusian Meeting on Discrete Mathematics
Discrete Applied Mathematics
Uploads
Papers by Juan Carlos Valenzuela Tripodoro