Numerical range of simple graphs and some bounds for their eigenvalues
Abstract
The numerical range of a simple graph G, named F(G), is the numerical
range of its adjacency matrix A(G). The main purpose of this paper was
to approximate F(G). Then, using this approximation, bounds for the largest
and the smallest eigenvalues of G were proposed. In fact, lower bounds for the largest eigenvalues of G were presented in terms of disjoint induced subgraphs of G and the numerical range of the square of A(G).
range of its adjacency matrix A(G). The main purpose of this paper was
to approximate F(G). Then, using this approximation, bounds for the largest
and the smallest eigenvalues of G were proposed. In fact, lower bounds for the largest eigenvalues of G were presented in terms of disjoint induced subgraphs of G and the numerical range of the square of A(G).
Keywords
graph theory; adjacency matrix; eigenvalue of graphs;numerical range
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.