• An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs 

      Abiad, Aida; Fiol Mora, Miquel Àngel; Haemers, Willem H.; Perarnau Llobet, Guillem (2014)
      Text en actes de congrés
      Accés obert
      We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by ...
    • Cospectral generalized Johnson and Grassmann graphs 

      Abiad, Aida; D'haeseleer, Jozefien; Simoens, Robin Nicolas (2022)
      Comunicació de congrés
      Accés obert
      Graphs with the same spectrum are called cospectral. A graph is determined by its spectrum if every graph cospectral with it is isomorphic to it. We ponder the question "Which graphs are determined by their spectrum?" for ...
    • La inversa de grupo del Laplaciano combinatorio en grafos distancia biregulares 

      Abiad, Aida; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José (2023)
      Text en actes de congrés
      Accés obert
      En este trabajo presentamos nuestra contribución al problema inverso para M –matrices en el caso de grafos distancia-biregulares. Dicho problema consiste en determinar cuándo la inversa de grupo del laplaciano combinatorio ...
    • On inertia and ratio type bounds for the k-independence number of a graph and their relationship 

      Abiad, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Zeijlemaker, Sjanne (Elsevier, 2023-07-15)
      Article
      Accés obert
      For , the -independence number of a graph is the maximum number of vertices that are mutually at distance greater than . The well-known inertia and ratio bounds for the (1-)independence number of a graph, due to Cvetković ...
    • On the k-independence number of graphs 

      Abiad, Aida; Coutinho, Gabriel; Fiol Mora, Miquel Àngel (2019-01-10)
      Article
      Accés obert
      This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than k. The previous bounds known in the ...
    • Optimization of eigenvalue bounds for the independence and chromatic number of graph powers 

      Abiad, Aida; Coutinho, Gabriel; Fiol Mora, Miquel Àngel; Nogueira, Bruno; Zeijlemaker, Shanne (2022-03)
      Article
      Accés obert
      The k-thpower of a graph G=(V,E), G^k, is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for ...
    • Some spectral and quasi-spectral characterizations of distance-regular graphs 

      Abiad, Aida; Van Dam, Edwin R; Fiol Mora, Miquel Àngel (2016-10-01)
      Article
      Accés obert
      In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular ...