28 citations · 52 across the 20 of their papers we have counts for
23 papers
Counting perfect edge dominating sets: extremal results and linear-time algorithms
Luciano N. Grippo, Min Chih Lin, Verónica Moyano +1
An edge of a graph \emph{dominates} itself and each edge adjacent to it. A \emph{perfect edge dominating set} is a subset of edges such that each edge outside the subset is dominat…
A Sharp Forbidden Interval for the Nontrivial Adjacency Eigenvalues of Trivially Perfect Graphs
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo
We prove a sharp forbidden interval for the nontrivial adjacency eigenvalues of trivially perfect graphs. More precisely, we show that if is a trivially perfect graph, then $\o…
Counting -convex sets in graphs
Mitre C. Dourado, Luciano N. Grippo, Min Chih Lin +1
We study the -convexity, the path convexity generated by all three-vertex paths, and focus on the problem of counting the -convex vertex sets of a graph , denoted by $…
Perfect Edge Domination in -free Graphs and in Graphs Without Efficient Edge Dominating Sets
Luciano N. Grippo, Min Chih Lin, Camilo Vera
An edge of a graph dominates itself along with any edge that shares an endpoint with it. An efficient edge dominating set (also called a dominating induced matching, DIM) is a subs…
Formulas and Upper Bounds for the Carath{é}odory Number of Hamming Graphs
Ezequiel Dratman, Lucía M. González, Luciano N. Grippo
Let be a simple graph and let be a subset of its vertices. We say that is -convex if every vertex that has at least two neighbors in also belongs…
Singularly cospectral circulant graphs
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo +1
Two graphs having the same spectrum are said to be cospectral. Two graphs such that the absolute values of their nonzero eigenvalues coincide are singularly cospectral graphs. Cosp…
On the spectral radius of unbalanced signed bipartite graphs
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo
A signed graph is one that features two types of edges: positive and negative. Balanced signed graphs are those in which all cycles contain an even number of positive edges. In the…
On restricted completions of chordal and trivially perfect graphs
Mitre C. Dourado, Luciano N. Grippo, Mario Valencia-Pabon
Let be a graph having a vertex such that is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to…
On the rank of the distance matrix of graphs
Ezequiel Dratman, Luciano N. Grippo, Verónica Moyano +1
Let be a connected graph with . The -entry of the distance matrix of is the distance between and . In this article, using…
On the generalized Helly property of hypergraphs, cliques, and bicliques
Mitre C. Dourado, Luciano N. Grippo, Martín D. Safe
A family of sets is -intersecting if every nonempty subfamily of or fewer sets has at least elements in its total intersection. A family of sets has the -Hell…
Finding singularly cospectral graphs
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo
Two graphs having the same spectrum are said to be cospectral. A pair of singularly cospectral graphs is formed by two graphs such that the absolute values of their nonzero eigenva…
On the spectral radius of block graphs having all their blocks of the same size
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo
Let be the class of block graphs on vertices having all their blocks of the same size. We prove that if has at most three pairwise ad…
Formulas in connection with parameters related to convexity of paths on three vertices: caterpillars and unit interval graphs
Lucía M. González, Luciano N. Grippo, Martín D. Safe
We present formulas to compute the P3-geodetic number, the P3-hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition,…
The determinant of the distance matrix of graphs with at most two cycles
Ezequiel Dratman, Luciano N. Grippo, Matín D. Safe +2
Let be a connected graph on vertices and its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known wh…
On the spectral radius of graphs: nonregular distance-hereditary graphs with given edge-connectivity, graphs with tree-width and block graphs with prescribed independence number
Cristian Conde, Ezequiel Dratman, Luciano N. Grippo
The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let the maximum degree of a graph and let be the spectral ra…
Covering graphs with convex sets and partitioning graphs into convex sets
Lucía M. González, Luciano N. Grippo, Martín D. Safe +1
We present some complexity results concerning the problems of covering a graph with convex sets and of partitioning a graph into convex sets. The following convexities are…
On nested and 2-nested graphs: two subclasses of graphs between threshold and split graphs
Nina Pardal, Guillermo A. Durán, Luciano N. Grippo +1
A -matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a $(0, 1)…
Partial characterization of graphs having a single large Laplacian eigenvalue
L. Emilio Allem, Antonio Cafure, Ezequiel Dratman +3
The parameter of a graph stands for the number of Laplacian eigenvalues greater than or equal to the average degree of . In this work, we address the problem of chara…
Domination parameters with number 2: interrelations and algorithmic consequences
Flavia Bonomo, Bostjan Bresar, Luciano N. Grippo +2
In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which…
Convex p-partitions of bipartite graphs
Luciano Grippo, Martín Matamala, Martín Safe +1
A set of vertices X of a graph G is convex if it contains all vertices on shortest paths between vertices of X. We prove that for fixed p, all partitions of the vertex set of a bip…
Forbidden Induced Subgraphs of Normal Helly Circular-Arc Graphs: Characterization and Detection
Yixin Cao, Luciano N. Grippo, Martín D. Safe
A normal Helly circular-arc graph is the intersection graph of arcs on a circle of which no three or less arcs cover the whole circle. Lin, Soulignac, and Szwarcfiter [Discrete App…
On circular-arc graphs having a model with no three arcs covering the circle
Luciano N. Grippo, Martín D. Safe
An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a f…
Graph classes with and without powers of bounded clique-width
Flavia Bonomo, Luciano N. Grippo, Martin Milanič +1
We initiate the study of graph classes of power-bounded clique-width, that is, graph classes for which there exist integers and such that the -th powers of the graphs…