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Conjectures on index and algebraic connectivity of graphs
- Source :
-
Linear Algebra & its Applications . Dec2010, Vol. 433 Issue 8-10, p1666-1673. 8p. - Publication Year :
- 2010
-
Abstract
- Abstract: Let be a simple graph with vertex set and edge set . The adjacency matrix of a graph is denoted by and defined as the matrix , where for and 0 otherwise. The largest eigenvalue () of is called the spectral radius or the index of . The Laplacian matrix of is , where is the diagonal matrix of its vertex degrees and is the adjacency matrix. Among all eigenvalues of the Laplacian matrix of a graph, the most studied is the second smallest, called the algebraic connectivity () of a graph [12]. In [1,2], Aouchiche et al. have given a series of conjectures on index () and algebraic connectivity () of (see also [3]). Here we prove two conjectures and disprove one by a counter example. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 433
- Issue :
- 8-10
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 53420108
- Full Text :
- https://doi.org/10.1016/j.laa.2010.06.012