Bounds for the energy of graphs

Kinkar Ch Das; Ivan Gutman

doi:10.15672/HJMS.20164513097

Bounds for the energy of graphs

Kinkar Ch Das
, Ivan Gutman

Department of Mathematics

University of Kragujevac

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

The energy of a graph G, denoted by E(G), is the sum of the absolute values of all eigenvalues of G. In this paper we present some lower and upper bounds for E(G) in terms of number of vertices, number of edges, and determinant of the adjacency matrix. Our lower bound is better than the classical McClelland’s lower bound. In addition, Nordhaus–Gaddum type results for E(G) are established.

Original language	English
Pages (from-to)	695-703
Number of pages	9
Journal	Hacettepe Journal of Mathematics and Statistics
Volume	45
Issue number	3
DOIs	https://doi.org/10.15672/HJMS.20164513097
State	Published - 2016

Keywords

Determinant of adjacency matrix
Energy (of graph)
Graph spectrum

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10.15672/HJMS.20164513097

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title = "Bounds for the energy of graphs",

abstract = "The energy of a graph G, denoted by E(G), is the sum of the absolute values of all eigenvalues of G. In this paper we present some lower and upper bounds for E(G) in terms of number of vertices, number of edges, and determinant of the adjacency matrix. Our lower bound is better than the classical McClelland{\textquoteright}s lower bound. In addition, Nordhaus–Gaddum type results for E(G) are established.",

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AU - Gutman, Ivan

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N2 - The energy of a graph G, denoted by E(G), is the sum of the absolute values of all eigenvalues of G. In this paper we present some lower and upper bounds for E(G) in terms of number of vertices, number of edges, and determinant of the adjacency matrix. Our lower bound is better than the classical McClelland’s lower bound. In addition, Nordhaus–Gaddum type results for E(G) are established.

AB - The energy of a graph G, denoted by E(G), is the sum of the absolute values of all eigenvalues of G. In this paper we present some lower and upper bounds for E(G) in terms of number of vertices, number of edges, and determinant of the adjacency matrix. Our lower bound is better than the classical McClelland’s lower bound. In addition, Nordhaus–Gaddum type results for E(G) are established.

KW - Determinant of adjacency matrix

KW - Energy (of graph)

KW - Graph spectrum

UR - https://www.scopus.com/pages/publications/84978766830

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DO - 10.15672/HJMS.20164513097

M3 - Article

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SP - 695

EP - 703

JO - Hacettepe Journal of Mathematics and Statistics

JF - Hacettepe Journal of Mathematics and Statistics

IS - 3

ER -

Bounds for the energy of graphs

Abstract

Keywords

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