Here we introduced the Modified Laplacian Schultz matrix and, as a result, the Modified Laplacian Schultz energy. We offered lower and upper bounds for the Modified Laplacian Schultz energy. For standard graphs such as complete bipartite graphs, star graphs, friendship graphs, crown graphs, complete graphs, and cocktail graphs, Modified Laplacian Schultz energies are estimated.
REFERENCES
1.
I.
Gutman
, The energy of a graph
, Ber. Math-Statist. Sekt. Forschungsz. Graz
, 103
, (1978
), 1
–22
.2.
I.
Gutman
and X.
Li
, J.
Zhang
, in Graph Energy, ed. by M.
Dehmer
, F.
Emmert-Streib
, Analysis of Complex Networks. From Biology to Linguistics
, (Wiley - VCH
, Weinheim
), (2009
), 145
–174
.3.
D.
Cvetković
and I.
Gutman
, Applications of Graph Spectra
, Mathematical Institution
, Belgrade
, (2009
).4.
D.
Cvetković
and I.
Gutman
, Selected Topics on Applications of Graph Spectra
, Mathematical Institution
, Belgrade
, (2011
).5.
I.
Gutman
, The energy of a graph: Old and New Results, ed. by A.
Betten
, A.
Kohnert
, R.
Laue
, A.
Wassermann
, Algebraic Combinatorics and Applications
, (Springer, Berlin
) (2001
), 196
–211
.6.
Huiqing
Liu
, Mei
Lu
and Feng
Tian
, Some upper bounds for the energy of graphs
, Journal of Mathematical Chemistry
, 41
(1
), (2007
), 45
–57
.7.
B.J.
MClelland
, Properties of the latent roots of a matrix: The estimation of π-electron energies
, J. Chem. Phys.
, 54
, (1971
), 640
–643
.8.
I.
Gutman
and B.
Zhou
, Laplacian energy of a graph
. Lin. Algebra Appl.
414
, 29
–37
(2006
)9.
H. P.
Schultz
, Topological organic chemistry. 1. Graph Theory and topological indices of alkanes
. J. Chem. Inf. Comput. Sci.
, 29
, (1989
), 227
–228
.10.
Klavz ar
and I.
Gutman
, Wiener number of vertex-weighted graphs and a chemical application
, Disc. Appl. Math.
, 80
(1997
), 73
–81
.11.
M. R. Rajesh
Kanna
and S.
Roopa
, Modified Schultz energy of graphs
, Advances in Mathematics: Scientific Journal
9
(2020
), no. 9
, 7149
–7164
.12.
R.B.
Bapat
and S.
Pati
, Energy of a graph is never an odd integer
, Bull. Kerala Math. Assoc.
, 1
, (2011
), 129
–132
.13.
B.J.
MClelland
, Properties of the latent roots of a matrix: The estimation of π-electron energies
, J. Chem. Phys.
, 54
, (1971
), 640
–643
.14.
15.
I. Ž.
Milovanović
, E. I.
Milovanović
and A.
Zakić
, A Short note on Graph Energy
, Commun. Math. Comput. Chem.
, 72
, (2014
), 179
–182
.
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