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Sharp Upper Bounds on the Spectral Radius of Graphs
, 2003
"... Let G be a simple connected graph with n vertices, m edges and degree sequence: d1 ≥ d2 · · · ≥ dn. The spectral radius ρ(G) of graph G is the largest eigenvalue of its adjacency matrix. In this paper, we present some sharp upper bounds of the spectral radius in terms of the degree sequence of gr ..."
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Let G be a simple connected graph with n vertices, m edges and degree sequence: d1 ≥ d2 · · · ≥ dn. The spectral radius ρ(G) of graph G is the largest eigenvalue of its adjacency matrix. In this paper, we present some sharp upper bounds of the spectral radius in terms of the degree sequence
Sharp upper bounds on the number of the scattering poles
"... We study the scattering poles of a compactly supported “black box ” perturbations of the Laplacian in Rn, n odd. We prove a sharp upper bound of the counting function N.r / modulo o.rn / in terms of the counting function of the reference operator in the smallest ball around the black box. In the mos ..."
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We study the scattering poles of a compactly supported “black box ” perturbations of the Laplacian in Rn, n odd. We prove a sharp upper bound of the counting function N.r / modulo o.rn / in terms of the counting function of the reference operator in the smallest ball around the black box
SHARP UPPER BOUNDS ON RESONANCES FOR PERTURBATIONS OF HYPERBOLIC SPACE
"... Abstract. For certain compactly supported metric and/or potential perturbations of the Laplacian on H n+1, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the radius of the unperturbed region in H n+1, and the volume of the ..."
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Cited by 4 (4 self)
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Abstract. For certain compactly supported metric and/or potential perturbations of the Laplacian on H n+1, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the radius of the unperturbed region in H n+1, and the volume
A Sharp Upper Bound for Region Unknotting Number of Torus KnotsI
"... Region crossing change for a knot or a proper link is an unknotting operation. In this paper, we provide a sharp upper bound on the region unknotting number for a large class of torus knots and proper links. Also, we discuss conditions on torus links to be proper. ..."
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Region crossing change for a knot or a proper link is an unknotting operation. In this paper, we provide a sharp upper bound on the region unknotting number for a large class of torus knots and proper links. Also, we discuss conditions on torus links to be proper.
A Sharp Upper Bound on Algebraic Connectivity Using Domination Number
"... Abstract Let G be a connected graph of order n. The algebraic connectivity of G is the second smallest eigenvalue of the Laplacian matrix of G. A dominating set in G is a vertex subset S such that each vertex of G that is not in S is adjacent to a vertex in S. The least cardinality of a dominating ..."
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set is the domination number. In this paper, we prove a sharp upper bound on the algebraic connectivity of a connected graph in terms of the domination number and characterize the associated extremal graphs. MSC: 05C35; 05C50
SHARP UPPER BOUNDS ON THE SPECTRAL RADIUS OF THE LAPLACIAN MATRIX OF GRAPHS
"... Abstract. Let G =(V,E) be a simple connected graph with n vertices and e edges. Assume that the vertices are ordered such that d1 ≥ d2 ≥... ≥ dn, wherediis the degree of vi for i =1, 2,...,nand the average of the degrees of the vertices adjacent to vi is denoted by mi. Letmmax be the maximum of mi’s ..."
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Cited by 1 (0 self)
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’s for i =1, 2,...,n.Also, let ρ(G) denote the largest eigenvalue of the adjacency matrix and λ(G) denotethe largest eigenvalue of the Laplacian matrix of a graph G. In this paper, we present a sharp upper bound on ρ(G): ρ(G) ≤ � 2e − (n − 1)dn +(dn − 1)mmax, with equality if and only if G is a star
A Sharp Upper Bound on the Approximation Order of Smooth Bivariate Pp Functions
 J. Approx. Theory
, 1993
"... Introduction It is the purpose of this note to show that the approximation order from the space \Pi ae k;\Delta of all piecewise polynomial functions in C ae of polynomial degree k on a triangulation \Delta of IR 2 is, in general, no better than k in case k ! 3ae + 2. This complements the res ..."
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Cited by 22 (5 self)
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Introduction It is the purpose of this note to show that the approximation order from the space \Pi ae k;\Delta of all piecewise polynomial functions in C ae of polynomial degree k on a triangulation \Delta of IR 2 is, in general, no better than k in case k ! 3ae + 2. This complements the result of [BH88] that the approximation order from \Pi ae k;\Delta for an arbitrary mesh \Delta is k + 1 if k 3ae + 2. Here, we define the approximation order of a space S of functions on IR 2 to be the largest real number r for which dist(f; oe h S) const f h r for any sufficiently smooth funct
Results 1  10
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