7 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, LucÃa 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…