TY - JOUR
T1 - On energy and laplacian energy of graphs
AU - Das, Kinkar Ch
AU - Mojallal, Seyed Ahmad
N1 - Publisher Copyright:
© 2016, International Linear Algebra Society (ILAS). All rights reserved.
PY - 2016/3
Y1 - 2016/3
N2 - Let G = (V,E) be a simple graph of order n with m edges. The energy of a graph G, denoted by ε(G), is defined as the sum of the absolute values of all eigenvalues of G. The Laplacian energy of the graph G is defined as (Formula presented), where μ1, μ2, …, μn−1, μn = 0 are the Laplacian eigenvalues of graph G. In this paper, some lower and upper bounds for ε(G) are presented in terms of number of vertices, number of edges, maximum degree and the first Zagreb index, etc. Moreover, a relation between energy and Laplacian energy of graphs is given.
AB - Let G = (V,E) be a simple graph of order n with m edges. The energy of a graph G, denoted by ε(G), is defined as the sum of the absolute values of all eigenvalues of G. The Laplacian energy of the graph G is defined as (Formula presented), where μ1, μ2, …, μn−1, μn = 0 are the Laplacian eigenvalues of graph G. In this paper, some lower and upper bounds for ε(G) are presented in terms of number of vertices, number of edges, maximum degree and the first Zagreb index, etc. Moreover, a relation between energy and Laplacian energy of graphs is given.
KW - Determinant
KW - Energy
KW - First Zagreb index
KW - Graph
KW - Laplacian energy
KW - Spectral radius
UR - https://www.scopus.com/pages/publications/84964039195
U2 - 10.13001/1081-3810.3272
DO - 10.13001/1081-3810.3272
M3 - Article
AN - SCOPUS:84964039195
SN - 1081-3810
VL - 31
SP - 167
EP - 186
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
IS - 1
M1 - 12
ER -