Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths

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 + root 5)/2)(2/k) when l = 3 and lambda(A) = 3(1/k) when l = 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.