On randić energy

Kinkar C.H. Das; Sezer Sorgun; Ivan Gutman

On randić energy

Kinkar C.H. Das
, Sezer Sorgun
, Ivan Gutman

Department of Mathematics

Nevsehir Haci Bektas Veli Universitesi
University of Kragujevac

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

31 Scopus citations

Abstract

Let G be a simple graph with n vertices and m edges. Let di be the degree of the i-th vertex of G. The Randić matrix R = (r_ij) is defined by r_ij = 1/√d_id_j if the i-th and j-th vertices are adjacent and r_ij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. Cavers et al. [On the normalized Laplacian energy and general Randić index R₁(G) of graphs, Lin. Algebra Appl. 433 (2010) 172-190] obtained some bounds on RE, but did not characterize the extremal graphs. We now find these extremal graphs. Additional lower and upper bounds for RE are obtained, in terms of n, m, maximum degree Δ, minimum degree δ, and the determinant of the adjacency matrix.

Original language	English
Pages (from-to)	81-92
Number of pages	12
Journal	Match
Volume	73
Issue number	1
State	Published - 2015

Cite this

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abstract = "Let G be a simple graph with n vertices and m edges. Let di be the degree of the i-th vertex of G. The Randi{\'c} matrix R = (rij) is defined by rij = 1/√didj if the i-th and j-th vertices are adjacent and rij = 0 otherwise. The Randi{\'c} energy RE is the sum of absolute values of the eigenvalues of R. Cavers et al. [On the normalized Laplacian energy and general Randi{\'c} index R1(G) of graphs, Lin. Algebra Appl. 433 (2010) 172-190] obtained some bounds on RE, but did not characterize the extremal graphs. We now find these extremal graphs. Additional lower and upper bounds for RE are obtained, in terms of n, m, maximum degree Δ, minimum degree δ, and the determinant of the adjacency matrix.",

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AU - Das, Kinkar C.H.

AU - Sorgun, Sezer

AU - Gutman, Ivan

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N2 - Let G be a simple graph with n vertices and m edges. Let di be the degree of the i-th vertex of G. The Randić matrix R = (rij) is defined by rij = 1/√didj if the i-th and j-th vertices are adjacent and rij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. Cavers et al. [On the normalized Laplacian energy and general Randić index R1(G) of graphs, Lin. Algebra Appl. 433 (2010) 172-190] obtained some bounds on RE, but did not characterize the extremal graphs. We now find these extremal graphs. Additional lower and upper bounds for RE are obtained, in terms of n, m, maximum degree Δ, minimum degree δ, and the determinant of the adjacency matrix.

AB - Let G be a simple graph with n vertices and m edges. Let di be the degree of the i-th vertex of G. The Randić matrix R = (rij) is defined by rij = 1/√didj if the i-th and j-th vertices are adjacent and rij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. Cavers et al. [On the normalized Laplacian energy and general Randić index R1(G) of graphs, Lin. Algebra Appl. 433 (2010) 172-190] obtained some bounds on RE, but did not characterize the extremal graphs. We now find these extremal graphs. Additional lower and upper bounds for RE are obtained, in terms of n, m, maximum degree Δ, minimum degree δ, and the determinant of the adjacency matrix.

UR - https://www.scopus.com/pages/publications/84922051371

M3 - Article

AN - SCOPUS:84922051371

SN - 0340-6253

VL - 73

SP - 81

EP - 92

JO - Match

JF - Match

IS - 1

ER -

On randić energy

Abstract

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