Numerical range of simple graphs and some bounds for their eigenvalues

Authors

  • Maliheh Tajarrod Department of Mathematics Kerman Branch, Islamic Azad University Kerman, Iran
  • Tahereh Sistani Department of Mathematics Kerman Branch, Islamic Azad University Kerman, Iran

DOI:

https://doi.org/10.30495/jme.v12i1.717

Keywords:

graph theory, adjacency matrix, eigenvalue of graphs, numerical range

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).

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Published

2018-06-29

Issue

Vol. 12

Section

Vol. 12, No. 4, (2018)

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