摘要
We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3, we show that the largest H-eigenvalue of its adjacency tensor is （（1 ＋ √-5）/2）2/k when = 3 and ）λ（A） = 31/k when g = 4, respectively. For the case of l ≥ 5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval （2, 3） when l≥ 5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.
We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3, we show that the largest H-eigenvalue of its adjacency tensor is （（1 ＋ √-5）/2）2/k when = 3 and ）λ（A） = 31/k when g = 4, respectively. For the case of l ≥ 5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval （2, 3） when l≥ 5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.
基金
Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11271221） and the Specialized Research Fund for State Key Laboratories.
