Graphs and matrices of maximal energy

By Vladimir Nikiforov. 2006

58 citations recorded by the source corpus.

Call the sum of the singular values of a matrix A the energy of A. We investigate graphs and matrices of energy close to the maximal one. We prove a conjecture of Koolen and Moulten and give a stability theorem characterizing all square nonnegative matrices and all graphs with energy close to the maximal one. In particular, such graphs are quasi-random.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3285558337fb84078cbb67bf2899f65189859b44

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Beyond graph energy: norms of graphs and matrices (2015, methodology): “For example, a simple construction using the Paley graphs [33] shows that F∗ (n) ≥ n √ n 2 − n.”
Spectra of digraphs (2010, background): “Nikiforov [87,88] extended the concept of energy to arbitrary real (or complex) matrices as follows: Let A be an n by m real matrix with, say, n m.”
On maximum degree energy of a graph (2009, background): “During these days the energy of a graph is a much studied quantity in the mathematical literature (See, for example, the recent papers [1,3,4,5,6,7]).”
ENERGY OF A GRAPH IS NEVER THE SQUARE ROOT OF AN ODD INTEGER (2008, background): “Nowadays the energy of graphs is a much studied quantity in the mathematical literature (see, for example, the recent papers [5, 6]).”