Back to Search
Start Over
On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs.
- Source :
-
Discrete Applied Mathematics . Jul2018, Vol. 243, p172-185. 14p. - Publication Year :
- 2018
-
Abstract
- Let G be a graph of order n . The energy E ( G ) of a simple graph G is the sum of absolute values of the eigenvalues of its adjacency matrix. The Laplacian energy, the signless Laplacian energy and the distance energy of graph G are denoted by L E ( G ) , S L E ( G ) and D E ( G ) , respectively. In this paper we introduce a distance Laplacian energy D L E and distance signless Laplacian energy D S L E of a connected graph. We present Nordhaus–Gaddum type bounds on Laplacian energy L E ( G ) and signless Laplacian energy S L E ( G ) in terms of order n of graph G and characterize graphs for which these bounds are best possible. The complete graph and the star give the smallest distance signless Laplacian energy D S L E among all the graphs and trees of order n , respectively. We give lower bounds on distance Laplacian energy D L E in terms of n for graphs and trees, and characterize the extremal graphs. Also we obtain some relations between D E , D S L E and D L E of graph G . Moreover, we give several open problems in this paper. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LAPLACIAN matrices
*GRAPH theory
*EIGENVALUES
*MATRICES (Mathematics)
*BOND graphs
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 243
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 129713651
- Full Text :
- https://doi.org/10.1016/j.dam.2018.01.004