Search

Your search keyword '"Hernández-Gómez, Juan C."' showing total 10 results
Start Over Author "Hernández-Gómez, Juan C." Search Limiters Available in Library Collection
10 results on '"Hernández-Gómez, Juan C."'

2. On the Total k-Domination in Graphs

Author

Bermudo Sergio, Hernández-Gómez Juan C., and Sigarreta José M.

Subjects
k-domination, total k-domination, k-tuple domination, k-tuple total domination, 05c69, Mathematics, QA1-939
Abstract

Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.

Published
2018
Full Text
View/download PDF

7. El Contraejemplo en la Elaboración de la Definición de Función Convexa por Estudiantes Universitarios

Author

Hernández-Gómez, Juan C., Locia-Espinoza, Edgardo, Morales-Carballo, Armando, and Sigarreta-Almira, José M.

Subjects
convex function, definición generada por prueba, función convexa, definition generated by proof, debate científico, counterexample, contraejemplo, scientific debate
Abstract

RESUMEN: En este artículo se reportan los resultados de una investigación que tuvo como objetivo identificar el papel que juega el contraejemplo en la elaboración de definiciones matemáticas. En particular se analizó el caso de la función convexa en un grupo de estudiantes de nivel universitario. Los elementos teóricos y metodológicos primarios que sustentaron el trabajo descansan en los aportes sobre pruebas y refutaciones, elementos de heurística, lenguaje y axiomática y en el debate científico en cursos de matemáticas. Como resultado fundamental se destaca que el debate científico favoreció mediante la discusión en torno al concepto de función convexa y a la formulación de contraejemplos. Estos contribuyeron en la comprobación de casos particulares, la formulación y refutación de conjeturas, hasta aproximarse a la presentación clásica de la definición. Establecemos también que el contraejemplo es un recurso didáctico y una herramienta mediadora que contribuye en los procesos de elaboración y comprensión de la definición matemática. ABSTRACT: In this paper the results of an investigation that aimed to identify the role played by the counterexample in the elaboration of mathematical definitions are reported. In particular, the case of the convex function; in a group of university students was analyzed. The principal theoretical and methodological elements that supported the work rest on the contributions in proof and refutations, elements of heuristics, language and axiomatics and in the scientific debate in mathematics courses. As a fundamental result, we emphasized that the scientific debate favored, through the discussion on the concept of convex function and the formulation of counterexamples These contributed to the verification of particular cases, the formulation and refutation of conjectures, until approaching the classic presentation of the definition. We also establish that the counterexample is a didactic resource and a mediation tool that contributes in the processes of elaboration and understanding of the mathematical definition.

Published
2019

8. On the inverse degree index and decompositions in graphs.

Author

Romero-Valencia, Jesús, Hernández-Gómez, Juan C., and Reyna-Hernández, Gerardo

Subjects
*GEOMETRIC vertices, *CHEMICAL structure, *SUBGRAPHS, *MATHEMATICAL decomposition
Abstract

The inverse degree index of a graph G=(V,E) without isolated vertices is defined as ID(G)=ΣvЄv1/dv, where dv is the degree of the vertex v in G. In this paper, we show a relation between the inverse degree of a graph and the inverse degree indices of the primary subgraphs obtained by a general decomposition of G, we establish some relations between the inverse degree index and other known indices and an application to a specific chemical structure is given. [ABSTRACT FROM AUTHOR]

Published
2019

10. Harmonic Index and Harmonic Polynomial on Graph Operations.

Author

Hernández-Gómez, Juan C., Méndez-Bermúdez, J. A., Rodríguez, José M., and Sigarreta, José M.

Subjects
*GRAPH algorithms, *COMPUTER algorithms, *LEXICOGRAPHICAL errors, *CHEMICALS, *POLYNOMIALS
Abstract

Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O (n 2) . [ABSTRACT FROM AUTHOR]

Published
2018
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results