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

Yıl 2018, Cilt: 1 Sayı: 1, 65 - 66, 30.09.2018

Rao Li

https://doi.org/10.33434/cams.443347

Öz

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.

Anahtar Kelimeler

Signless Laplacian Eigenvalues, Hamiltonian Properties

Kaynakça

• [1] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York (1976).
• [2] K. C. Das, Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs, Discrete Mathematics 312 (2012) 992 – 998.