Paper Info
Title
A method for computing local contributions to graph energy based on Estrada-Benzi approach.
Abstract
The graph energy, as a graph invariant, contains very important structural information about the graph, its subgraphs, and ingredient segments. Estrada and Benzi (2017) have shown that the graph energy can be extracted from the weighted sum of the traces of the even powers of its adjacency matrix. Based on this kind of representation, they have reported newer and more precise bounds of the energy as the sum of fragments’ contributions such as Cn (cycles of length n), Pn (path graph), Sn (star graph), Dn (diamond graph), F (a subgraph containing a square with a pendant vertex), and H (a subgraph containing two triangles with a shared vertex). In this paper, inspired by the work of Estrada and Benzi, we first introduce a general formula for calculating the contribution of subgraphs to the total energy of the graph. We also compute the boundaries of the contributions of the above subgraphs and some of the subgraphs that appear for the first time in the higher traces of the adjacency matrix of the graph. Further, we calculate the upper bound of the graph energy for cyclic and fullerene graphs with higher accuracy.
Year
DOI
Venue
2019
10.1016/j.dam.2019.01.011
Discrete Applied Mathematics
Keywords
Field
DocType
Graph energy,Graph spectra,Conjugated molecules,Matrix functions
Adjacency matrix,Discrete mathematics,Combinatorics,Graph energy,Diamond graph,Graph property,Vertex (geometry),Upper and lower bounds,Star (graph theory),Mathematics,Path graph
Journal
Volume
ISSN
Citations 
260
0166-218X
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Farshad Safaei19519.37
F. Kashkooei Jahromi200.34
S. Fathi300.34