On the Laplacian and Signless Laplacian Spectra of Complete Multipartite Graphs - Abdussakir, Abdussakir; Sandhya Elya Ikawati, Deasy; Nirmala Sari, F. Kurnia (Proceedings of the International Conference on Green Technology; Vol 8 No 1 (2017): Proceedings of the International Conference on Green Technology, 2017)
Let G be a finite simple graph with vertex set V ( G ) = { v 1 , v 2 , v 3 , …, v n } and edge set E ( G ). The adjacency matrix of G is an ( n ´ n )-matrix A ( G ) = [ a ij ] where a ij = 1 if v i v j Î E ( G ) and a ij = 0 elsewhere, and the degree matrix of G is a diagonal ( n ´ n )-matrix D ( G ) = [ d ij ] where d ii = deg G ( v i ) and d ij = 0 for i ≠ j . The Laplacian matrix of G is L ( G ) = D ( G ) – A ( G ) and the signless Laplacian matrix of G is Q ( G ) = D ( G ) + A ( G ). The study of spectrum of Laplacian and signless Laplacian matrix of graph are interesting topic till today. In this paper, we determine the Laplacian and signless Laplacian spectra of complete multipartite graphs.