8 research outputs found
Some new aspects of main eigenvalues of graphs
An eigenvalue of the adjacency matrix of a graph is said to be main if the all-1 vector is non-orthogonal to the associated eigenspace. This paper explores some new aspects of the study of main eigenvalues of graphs, investigating specifically cones over strongly regular graphs and graphs for which the least eigenvalue is non-main. In this case, we characterize paths and trees with diameter-3 satisfying the property. We may note that the importance of
least eigenvalues of graphs for the equilibria of social and economic networks was recently uncovered in literature.publishe
Unicyclic graphs with exactly two main eigenvalues
www.elsevier.com/locate/aml An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero, and it is well known that a graph has exactly one main eigenvalue if and only if it is regular. In this work, all connected unicyclic graphs with exactly two main eigenvalues are determined. c â—‹ 2006 Elsevier Ltd. All rights reserved