On the difference of energies of a graph and its complement graph

On the difference of energies of a graph and its complement graph

The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. In this paper we study the difference of energies of a (regular) graph G and its complete graph G‾, that is, E(G)−E(G‾). In particular, we provide the answer to Problem 12 raised in Nikifo...

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Veröffentlicht in:Linear algebra and its applications 2020-06, Vol.595, p.1-12
Hauptverfasser: Mojallal, Seyed Ahmad, Hansen, Pierre
Format: Artikel
Sprache:eng
Schlagworte:
Complement graph
Eigenvalues
Graph energy
Linear algebra
Lower bounds
Regular graph
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Beschreibung
Zusammenfassung:The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. In this paper we study the difference of energies of a (regular) graph G and its complete graph G‾, that is, E(G)−E(G‾). In particular, we provide the answer to Problem 12 raised in Nikiforov (2016) [18]. Moreover, we give a lower bound for the energy of a regular graph in terms of the order and the clique cover number.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.02.026