On incidence energy of graphs

Kinkar Ch Das; Ivan Gutman

doi:10.1016/j.laa.2013.12.026

On incidence 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

Let G=(V,E) be a simple graph with vertex set V={^v1, ^v2,.,^vn} and edge set E={^e1, ^e2,.,^em}. The incidence matrix I(G) of G is the n×m matrix whose (i,j)-entry is 1 if ^vi is incident to ^ej and 0 otherwise. The incidence energy IE of G is the sum of the singular values of I(G). In this paper we give lower and upper bounds for IE in terms of n, m, maximum degree, clique number, independence number, and the first Zagreb index. Moreover, we obtain Nordhaus-Gaddum-type results for IE.

Original language	English
Pages (from-to)	329-344
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	446
DOIs	https://doi.org/10.1016/j.laa.2013.12.026
State	Published - 1 Apr 2014

Keywords

Energy (of matrix)
Graph spectrum
Incidence energy
Incidence matrix
Laplacian spectrum (of graph)

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title = "On incidence energy of graphs",

abstract = "Let G=(V,E) be a simple graph with vertex set V=\{v1, v2,.,vn\} and edge set E=\{e1, e2,.,em\}. The incidence matrix I(G) of G is the n×m matrix whose (i,j)-entry is 1 if vi is incident to ej and 0 otherwise. The incidence energy IE of G is the sum of the singular values of I(G). In this paper we give lower and upper bounds for IE in terms of n, m, maximum degree, clique number, independence number, and the first Zagreb index. Moreover, we obtain Nordhaus-Gaddum-type results for IE.",

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AU - Das, Kinkar Ch

AU - Gutman, Ivan

PY - 2014/4/1

Y1 - 2014/4/1

N2 - Let G=(V,E) be a simple graph with vertex set V={v1, v2,.,vn} and edge set E={e1, e2,.,em}. The incidence matrix I(G) of G is the n×m matrix whose (i,j)-entry is 1 if vi is incident to ej and 0 otherwise. The incidence energy IE of G is the sum of the singular values of I(G). In this paper we give lower and upper bounds for IE in terms of n, m, maximum degree, clique number, independence number, and the first Zagreb index. Moreover, we obtain Nordhaus-Gaddum-type results for IE.

AB - Let G=(V,E) be a simple graph with vertex set V={v1, v2,.,vn} and edge set E={e1, e2,.,em}. The incidence matrix I(G) of G is the n×m matrix whose (i,j)-entry is 1 if vi is incident to ej and 0 otherwise. The incidence energy IE of G is the sum of the singular values of I(G). In this paper we give lower and upper bounds for IE in terms of n, m, maximum degree, clique number, independence number, and the first Zagreb index. Moreover, we obtain Nordhaus-Gaddum-type results for IE.

KW - Energy (of matrix)

KW - Graph spectrum

KW - Incidence energy

KW - Incidence matrix

KW - Laplacian spectrum (of graph)

UR - https://www.scopus.com/pages/publications/84894281046

U2 - 10.1016/j.laa.2013.12.026

DO - 10.1016/j.laa.2013.12.026

M3 - Article

AN - SCOPUS:84894281046

SN - 0024-3795

VL - 446

SP - 329

EP - 344

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On incidence energy of graphs

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Keywords

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