1. Relation between signless Laplacian energy, energy of graph and its line graph.
- Author
-
Das, Kinkar Ch. and Mojallal, Seyed Ahmad
- Subjects
- *
LAPLACIAN matrices , *GRAPH theory , *ABSOLUTE value , *MATHEMATICAL bounds , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
The energy of a simple graph G , E ( G ) , is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by E ( L G ) ( L G is the line graph of G ) and LE + ( G ) , respectively. In this paper we obtain a relation between E ( L G ) and LE + ( G ) of graph G . From this relation we characterize all the graphs satisfying E ( L G ) = LE + ( G ) + 4 m n − 4 . We also present a relation between E ( G ) and E ( L G ) . Moreover, we give an upper bound on E ( L G ) of graph G and characterize the extremal graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF