The sum of the largest and smallest signless laplacian eigenvalues and some Hamiltonian properties of graphs

Authors : Rao Lİ

Pages : 65-66

Doi:10.33434/cams.443347

View : 18 | Download : 13

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :The signless Laplacian eigenvalues of a graph $G$ are eigenvalues of the matrix $Qinsert ignore into journalissuearticles values(G); = Dinsert ignore into journalissuearticles values(G); + Ainsert ignore into journalissuearticles values(G);$, where $Dinsert ignore into journalissuearticles values(G);$ is the diagonal matrix of the degrees of the vertices in $G$ and $Ainsert ignore into journalissuearticles values(G);$ 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