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Total Outer-Independent Domination Number: Bounds and Algorithms
(MDPI AG, 2025-03-10)
BOSCH PÉREZ, PAUL JESÚS
;
Ernesto Parra Inza
;
Ismael Rios Villamar
;
José Luis Sánchez-Santiesteban
In graph theory, the study of domination sets has garnered significant interest due to its applications in network design and analysis. Consider a graph G(V,E); a subset of its vertices is a total dominating set (TDS) if, for each x∈V(G), there exists an edge in E(G) connecting x to at least one vertex within this subset. If the subgraph induced by the vertices outside the TDS has no edges, the set is called a total outer-independent dominating set (TOIDS). The total outer-independent domination number, denoted as γtoi(G), represents the smallest cardinality of such a set. Deciding if a given graph has a TOIDS with at most r vertices is an NP-complete problem. This study introduces new lower and upper bounds for γtoi(G) and presents an exact solution approach using integer linear programming (ILP). Additionally, we develop a heuristic and a procedure to efficiently obtain minimal TOIDS.
3
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A Methodology for the Analysis of Soccer Matches Based on PageRank Centrality
(2017)
Julio Rojas-Mora
;
CHAVEZ BUSTAMANTE, FELIPE ORLANDO
;
Nicolás Medina-Valdebenito
;
Julio del Río-Andrade
Scopus© Citations 6 3
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On the variable inverse sum deg index
(2023)
Edil D. Molina
;
BOSCH PÉREZ, PAUL JESÚS
;
José M. Sigarreta
;
Eva Tourís
Several important topological indices studied in mathematical chemistry are expressed in the following way Puv∈E(G) F(du, dv), where F is a two variable function that satisfies the condition F(x, y) = F(y, x), uv denotes an edge of the graph G and du is the degree of the vertex u. Among them, the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dua + dva), was found to have several applications. In this paper, we solve some problems posed by Vukičević [1], and we characterize graphs with maximum and minimum values of the ISDa index, for a < 0, in the following sets of graphs with n vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons. © 2023 the Author(s), licensee AIMS Press.
8 1Scopus© Citations 2
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Fast and compact planar embeddings
(2020)
FERRES, LEONARDO ADRIÁN
;
José Fuentes-Sepúlveda
;
Travis Gagie
;
Meng He
;
Gonzalo Navarro
9Scopus© Citations 16

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