Fundamenta Informaticae - Volume 185, issue 3

Authors: Cabrera Martínez, A. | García-Gómez, C. | Rodríguez-Velázquez, J. A.

Article Type: Research Article

Abstract: The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters. The picture is quite different when it concerns the perfect Roman domination number. In this case, we obtain general bounds and then we give sufficient and/or necessary conditions for the bounds to be achieved. We also discuss the case of perfect Roman graphs and we characterize the lexicographic product graphs where the perfect …Roman domination number equals the Roman domination number. Show more

Keywords: Roman domination, perfect domination, perfect Roman domination, lexicographic product

DOI: 10.3233/FI-222108

Citation: Fundamenta Informaticae, vol. 185, no. 3, pp. 201-220, 2022

Authors: Jiménez González, Jesús Arturo

Article Type: Research Article

Abstract: Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are ℤ-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type 𝔸r (for r ≥ 1), within the framework introduced in [Fundamenta Informaticae 184 (1):49–82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.

Keywords: Integral quadratic form, Gram congruence, Dynkin type, Coxeter polynomial, edgebipartite graph, quiver, incidence matrix, signed line graph, 2020 MSC: 15A63, 15A21, 15B36, 05C22, 05C50, 05C76, 05B20

DOI: 10.3233/FI-222109

Citation: Fundamenta Informaticae, vol. 185, no. 3, pp. 221-246, 2022

Authors: Schmidt-Schauß, Manfred | Kutsia, Temur | Levy, Jordi | Villaret, Mateu | Kutz, Yunus

Article Type: Research Article

Abstract: A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables …representing partial letrec-environments is also shown to be in NP. Show more

Keywords: Nominal unification, lambda calculus, higher-order expressions, recursive let, atom variables

DOI: 10.3233/FI-222110

Citation: Fundamenta Informaticae, vol. 185, no. 3, pp. 247-283, 2022