On Orderenergetic Graphs

Let G be a simple graph of order n. The eigenvalue of a graph G is the eigenvalue of its adjacency matrix. The energy E(G) of G is the sum of absolute values of its eigenvalues. A graph G of order n is orderenergetic if E(G) = n. The algebraic multiplicity of the number zero in the spectrum of G is...

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Bibliographic Details
Published in:Match (Mülheim) 2024, Vol.92 (1), p.73-88
Main Authors: Rakshith, B.R., Das, Kinkar Chandra
Format: Article
Language:English
Online Access:Get full text
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Summary:Let G be a simple graph of order n. The eigenvalue of a graph G is the eigenvalue of its adjacency matrix. The energy E(G) of G is the sum of absolute values of its eigenvalues. A graph G of order n is orderenergetic if E(G) = n. The algebraic multiplicity of the number zero in the spectrum of G is referred to as its nullity, and is denoted by η. In this paper, we show that if the cycle C4 is not an induced subgraph of a graph G with nullity η = 3, then G is not orderenergetic. We also obtain some results connecting orderenergetic graphs and minimum degree. Finally, we show that there is a connected orderenergetic graph on 10k + 8 vertices for all k ≥ 0.
ISSN:0340-6253
DOI:10.46793/match.92-1.073R