Geodesic
Laplacian Energy of Union and Cartesian Product and Laplacian Equienergetic Graphs
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 193

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The Laplacian energy of a graph $G$ with $n$ vertices and $m$ edges is defined as $LE(G) = \sum_{i=1}^{n}\left|\mu_i - 2m/n \right|$, where $\mu_1,\mu_2,\ldots,\mu_n$ are the Laplacian eigenvalues of $G$. If two graphs $G_1$ and $G_2$ have equal average vertex degrees, then $LE(G_1 \cup G_2) = LE(G_1) + LE(G_2)$. Otherwise, this identity is violated. We determine a term $\Xi$, such that $LE(G_1) + LE(G_2)-\Xi \leq LE(G_1 \cup G_2) \leq LE(G_1) + LE(G_2) +\Xi$ holds for all graphs. Further, by calculating $LE$ of the Cartesian product of some graphs, we construct new classes of Laplacian non-cospectral, Laplacian equienergetic graphs.
Classification : 05C50, 05C75
Keywords: Laplacian spectrum, Laplacian energy, Cartesian product, Laplacian equienergetic graphs 
@article{KJM_2015_39_2_a7,
     author = {Harishchandra S. Ramane and Gouramma A. Gudodagi and Ivan Gutman},
     title = {Laplacian {Energy} of {Union} and {Cartesian} {Product} and {Laplacian} {Equienergetic} {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {193 },
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a7/}
}
TY  - JOUR
AU  - Harishchandra S. Ramane
AU  - Gouramma A. Gudodagi
AU  - Ivan Gutman
TI  - Laplacian Energy of Union and Cartesian Product and Laplacian Equienergetic Graphs
JO  - Kragujevac Journal of Mathematics
PY  - 2015
SP  - 193 
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a7/
LA  - en
ID  - KJM_2015_39_2_a7
ER  - 
%0 Journal Article
%A Harishchandra S. Ramane
%A Gouramma A. Gudodagi
%A Ivan Gutman
%T Laplacian Energy of Union and Cartesian Product and Laplacian Equienergetic Graphs
%J Kragujevac Journal of Mathematics
%D 2015
%P 193 
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a7/
%G en
%F KJM_2015_39_2_a7
Harishchandra S. Ramane; Gouramma A. Gudodagi; Ivan Gutman. Laplacian Energy of Union and Cartesian Product and Laplacian Equienergetic Graphs. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 193 . http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a7/