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Bounds on graph energy

Author(s)

Ivan Gutman Faculty of Science, University of Kragujevac,Kragujevac 34000,Serbia

Mohammad Reza Oboudi Department of Mathematics, College of Sciences, Shiraz University,Shiraz 71457-44776,Iran

Abstract

Let G be a graph of order n and size m, and its eigenvalues i ; i = 1; : : : ; n, be labeled so that j1j j2j jnj. The energy E(G) of G is the sum of absolute values of its eigenvalues. It was recently shown that for t = 1, 2m t + |λ1||λn| n|λ1| + |λn| is a lower bound on E(G). We now establish conditions under which for t > 1, this expression is an upper bound on E(G).We also show that for a class of r-regular graphs, E(G) ≥ 2rn/(r + 1), and determine the equality cases.

Publication Details

Page(s) 1-4

DOI DOI not available

Published Journal: Discrete Mathematics Letters, Volume: 4, Issue: 0, Year: 2020

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Keywords

energy (of graph), spectrum (of graph), eigenvalue (of graph)., graph energy

References

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