Energy of Graphs, Matroids and Fibonacci Numbers

Author(s):

Saeid Alikhani , Mohammad A. Iranmanesh

Abstract:
The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.
Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:5 Issue: 2, Nov 2010
Pages:
55 to 60
https://www.magiran.com/p786954  
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