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Degree-based energies of graphs.
- Source :
-
Linear Algebra & its Applications . Oct2018, Vol. 554, p185-204. 20p. - Publication Year :
- 2018
-
Abstract
- Let G = ( V , E ) be a simple graph of order n and size m , with vertex set V ( G ) = { v 1 , v 2 , … , v n } , without isolated vertices and sequence of vertex degrees Δ = d 1 ≥ d 2 ≥ ⋯ ≥ d n = δ > 0 , d i = d G ( v i ) . If the vertices v i and v j are adjacent, we denote it as v i v j ∈ E ( G ) or i ∼ j . With TI we denote a topological index that can be represented as T I = T I ( G ) = ∑ i ∼ j F ( d i , d j ) , where F is an appropriately chosen function with the property F ( x , y ) = F ( y , x ) . A general extended adjacency matrix A = ( a i j ) of G is defined as a i j = F ( d i , d j ) if the vertices v i and v j are adjacent, and a i j = 0 otherwise. Denote by f i , i = 1 , 2 , … , n the eigenvalues of A . The “energy” of the general extended adjacency matrix is defined as E T I = E T I ( G ) = ∑ i = 1 n | f i | . Lower and upper bounds on E T I are obtained. By means of the present approach a plethora of earlier established results can be obtained as special cases. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 554
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 131112934
- Full Text :
- https://doi.org/10.1016/j.laa.2018.05.027