AbstractDenote by λ2(T) the second largest eigenvalue of a tree T. An easy algorithm is given to decide whether λ2(T)⩽λ for a given number λ, and a structure theorem for trees withλ2(T)⩽λ is proved. Also, it is shown that a tree T with n vertices has λ2(T)⩽lsqb(n−3)2rsqb12; this bound is best possible for odd n
AbstractLet λk(F) be the kth largest eigenvalue of a forest F, and λ(F) be the smallest positive eig...
AbstractWe consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue λk.o...
AbstractWe determine all trees whose second largest eigenvalue does not exceed 2. Next, we consider ...
AbstractVery little is known about upper bounds for the largest eigenvalues of a tree that depend on...
AbstractDenote by λ2(T) the second largest eigenvalue of a tree T. An easy algorithm is given to dec...
AbstractVery little is known about upper bounds for the largest eigenvalues of a tree that depend on...
AbstractWe consider the only remaining unsolved case n ≡ 0(mod k) for the largest kth eigenvalue of ...
AbstractLet λk(T) be the kth eigenvalue of a tree, [x] the largest integer not greater than x. It is...
AbstractIn this paper, we investigated a conjecture [Linear Algebra Appl. 283 (1998) 247] about the ...
AbstractThe set of trees with n vertices and the set of trees with perfect matchings are denoted by ...
AbstractVery little is known about lower bounds and upper bounds for the second largest Laplacian ei...
AbstractWe prove the upper bound λk(T) ⩽ √[n / k] – 1 for the kth largest eigenvalue of a tree T (1 ...
AbstractWe consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue of t...
AbstractIn this paper, we present an upper bound for the second largest eigenvalue of a tree on n=2k...
AbstractIn this paper, an upper bound and a tight lower bound for the second largest eigenvalue of a...
AbstractLet λk(F) be the kth largest eigenvalue of a forest F, and λ(F) be the smallest positive eig...
AbstractWe consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue λk.o...
AbstractWe determine all trees whose second largest eigenvalue does not exceed 2. Next, we consider ...
AbstractVery little is known about upper bounds for the largest eigenvalues of a tree that depend on...
AbstractDenote by λ2(T) the second largest eigenvalue of a tree T. An easy algorithm is given to dec...
AbstractVery little is known about upper bounds for the largest eigenvalues of a tree that depend on...
AbstractWe consider the only remaining unsolved case n ≡ 0(mod k) for the largest kth eigenvalue of ...
AbstractLet λk(T) be the kth eigenvalue of a tree, [x] the largest integer not greater than x. It is...
AbstractIn this paper, we investigated a conjecture [Linear Algebra Appl. 283 (1998) 247] about the ...
AbstractThe set of trees with n vertices and the set of trees with perfect matchings are denoted by ...
AbstractVery little is known about lower bounds and upper bounds for the second largest Laplacian ei...
AbstractWe prove the upper bound λk(T) ⩽ √[n / k] – 1 for the kth largest eigenvalue of a tree T (1 ...
AbstractWe consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue of t...
AbstractIn this paper, we present an upper bound for the second largest eigenvalue of a tree on n=2k...
AbstractIn this paper, an upper bound and a tight lower bound for the second largest eigenvalue of a...
AbstractLet λk(F) be the kth largest eigenvalue of a forest F, and λ(F) be the smallest positive eig...
AbstractWe consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue λk.o...
AbstractWe determine all trees whose second largest eigenvalue does not exceed 2. Next, we consider ...
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