Title of article :
Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues
Author/Authors :
Tajarrod, M Kerman Branch - Islamic Azad University , Sistani, T Kerman Branch - Islamic Azad University
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 is to approximate F(G). Then, using this approximation,
bounds for the largest and the smallest eigenvalues of G are proposed. In
fact, lower bounds for the largest eigenvalues of G are 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
Journal title :
Astroparticle Physics
