Extremal graphs for Randić energy

Kinkar Ch Das; Shaowei Sun

Extremal graphs for Randić energy

Kinkar Ch Das
, Shaowei Sun

Department of Mathematics

Sungkyunkwan University

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

10 Scopus citations

Abstract

The Randić matrix R(G) = (r_ij)_nxn of a graph G whose vertex v_i has degree d_i is defined by r_ij = 1/√d_id_j if the vertices v_i and v_j are adjacent and r_ij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R(G). In MATCH Commun. Math. Comput. Chem. 74 (2015) 367-387, Maden obtained several bounds on Randić energy and characterized the extremal graphs. We found some errors in the characterization of extremal graphs. Some of these are now corrected, whereas some are stated as conjectures.

Original language	English
Pages (from-to)	77-84
Number of pages	8
Journal	Match
Volume	77
Issue number	1
State	Published - 2017

Cite this

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abstract = "The Randi{\'c} matrix R(G) = (rij)nxn of a graph G whose vertex vi has degree di is defined by rij = 1/√didj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randi{\'c} energy RE is the sum of absolute values of the eigenvalues of R(G). In MATCH Commun. Math. Comput. Chem. 74 (2015) 367-387, Maden obtained several bounds on Randi{\'c} energy and characterized the extremal graphs. We found some errors in the characterization of extremal graphs. Some of these are now corrected, whereas some are stated as conjectures.",

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AB - The Randić matrix R(G) = (rij)nxn of a graph G whose vertex vi has degree di is defined by rij = 1/√didj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R(G). In MATCH Commun. Math. Comput. Chem. 74 (2015) 367-387, Maden obtained several bounds on Randić energy and characterized the extremal graphs. We found some errors in the characterization of extremal graphs. Some of these are now corrected, whereas some are stated as conjectures.

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Extremal graphs for Randić energy

Abstract

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