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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…
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…
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…
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…
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…