Bounds for the Energy of Graphs

Xueliang Li, Yongtang Shi and Ivan Gutman
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Xueliang Li: Nankai University, Center for Combinatorics
Yongtang Shi: Nankai University, Center for Combinatorics
Ivan Gutman: University of Kragujevac, Faculty of Science

Chapter Chapter 5 in Graph Energy, 2012, pp 59-81 from Springer

Abstract: Abstract A graph G of order n and size m is called an (n, m)-graph. In what follows we assume that the graph eigenvalues are labeled in a nonincreasing manner, i.e., λ1≥λ2≥⋯≥λ n . If G is connected, then λ1>λ2 [81]. Because λ1≥|λ i |,i=2,…,n, the eigenvalue λ1 is referred to as the spectral radius of G. Three well-known relations for the eigenvalues are 5.1 $$\begin{array}{rcl} & & \sum\limits_{i=1}^{n}{\lambda }_{ i} = 0\end{array}$$ 5.2 $$\begin{array}{rcl} & & \sum\limits_{i=1}^{n}{\lambda }_{ i}^{2} = 2m\end{array}$$ 5.3 $$\begin{array}{rcl} & & \sum\limits_{i

Keywords: Bipartite Graph; Spectral Radius; Regular Graph; Cayley Graph; Hermitian Matrix (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-4220-2_5

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