Fundamenta Informaticae - Volume 185, issue 2

Authors: Bača, Martin | Semaničová-Feňovčíková, Andrea | Lai, Ruei-Ting | Wang, Tao-Ming

Article Type: Research Article

Abstract: Let G = (V , E ) be a finite simple undirected graph without K 2 components. A bijection f : E → {1, 2, ⋯, |E |} is called a local antimagic labeling if for any two adjacent vertices u and v , they have different vertex sums, i.e., w (u ) ≠ w (v ), where the vertex sum w (u ) = ∑e ∈E (u ) f (e ), and E (u ) is the set of edges incident to u . Thus any local antimagic labeling induces a proper vertex …coloring of G where the vertex v is assigned the color (vertex sum) w (v ). The local antimagic chromatic number χla (G ) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G . It was conjectured [6] that for every tree T the local antimagic chromatic number l + 1 ≤ χla (T ) ≤ l + 2, where l is the number of leaves of T . In this article we verify the above conjecture for complete full t -ary trees, for t ≥ 2. A complete full t -ary tree is a rooted tree in which all nodes have exactly t children except leaves and every leaf is of the same depth. In particular we obtain that the exact value for the local antimagic chromatic number of all complete full t -ary trees is l + 1 for odd t . Show more

Keywords: antimagic labeling, local antimagic labeling, local antimagic chromatic number, complete full t-ary tree

DOI: 10.3233/FI-222105

Citation: Fundamenta Informaticae, vol. 185, no. 2, pp. 99-113, 2022

Authors: Danvy, Olivier

Article Type: Research Article

Abstract: “There and Back Again” (TABA) is a programming pattern where the recursive calls traverse one data structure and the subsequent returns traverse another. This article presents new TABA examples, refines existing ones, and formalizes both their control flow and their data flow using the Coq Proof Assistant. Each formalization mechanizes a pen-and-paper proof, thus making it easier to “get” TABA. In addition, this article identifies and illustrates a tail-recursive variant of TABA, There and Forth Again (TAFA) that does not come back but goes forth instead with more tail calls.

Keywords: TABA, recursion pattern, list processing, symbolic convolutions, eta redexes, Coq Proof Assistant, There and Forth Again (TAFA), defunctionalization and refunctionalization, lambda-lifting and lambda-dropping, lightweight fusion and lightweight fission, continuations

DOI: 10.3233/FI-222106

Citation: Fundamenta Informaticae, vol. 185, no. 2, pp. 115-183, 2022

Authors: Garzón, Ester M. | Martínez, José A. | Moreno, Juan J. | Puertas, María L.

Article Type: Research Article

Abstract: Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph. This is the situation of the domination number, the Roman domination number or the 2-domination number, among others. Contrary to what happens with the domination number and the Roman domination number, the 2-domination number remains unknown in cylinders, that is, the Cartesian product of a cycle and a path and in this paper, we will compute this parameter in the cylinders with small cycles. We will develop two algorithms involving the (min, …+) matrix product that will allow us to compute the desired values of γ2(Cn □Pm ), with 3 ≤ n ≤ 15 and m ≤ 2. We will also pose a conjecture about the general formula for the 2-domination number in this graph class. Show more

Keywords: 2-domination, Cartesian product, (min, +) matrix product

DOI: 10.3233/FI-222107

Citation: Fundamenta Informaticae, vol. 185, no. 2, pp. 185-199, 2022