- Communications in Advanced Mathematical Sciences
- Vol: 1 Issue: 1
- The sum of the largest and smallest signless laplacian eigenvalues and some Hamiltonian properties o...
The sum of the largest and smallest signless laplacian eigenvalues and some Hamiltonian properties of graphs
Authors : Rao Li
Pages : 65-66
Doi:10.33434/cams.443347
View : 8 | Download : 4
Publication Date : 2018-09-30
Article Type : Research
Abstract :The signless Laplacian eigenvalues of a graph $G$ are eigenvalues of the matrix $Q(G) = D(G) + A(G)$, where $D(G)$ is the diagonal matrix of the degrees of the vertices in $G$ and $A(G)$ is the adjacency matrix of $G$. Using a result on the sum of the largest and smallest signless Laplacian eigenvalues obtained by Das in \cite{Das}, we in this note present sufficient conditions based on the sum of the largest and smallest signless Laplacian eigenvalues for some Hamiltonian properties of graphs.Keywords : Signless Laplacian Eigenvalues, Hamiltonian Properties