A sharp lower bound of the spectral radius with application to the energy of a graph

2021 ◽  
Vol 293 ◽  
pp. 59-63
Author(s):  
Ji-Ming Guo ◽  
Meng-Ni Yu
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Sharp Lower Bound

scholarly journals A sharp lower bound of the spectral radius of simple graphs

2009 ◽  
Vol 3 (2) ◽  
pp. 379-385 ◽  
Author(s):  
Shengbiao Hu
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Connected Graph ◽  
Simple Graphs ◽  
Degree Of Vertex ◽  
Simple Connected Graph ◽  
Two Parameter ◽  
Sharp Lower Bound

Let G be a simple connected graph with n vertices and let p(G) be its spectral radius. The 2-degree of vertex i is denoted by ti, which is the sum of degrees of the vertices adjacent to i. Let Ni = ?j~i tj and Mi = ?j~i Nj. We find a sharp lower bound of p(G), which only contains two parameter Ni and Mi. Our result extends recent known results.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

scholarly journals A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter

2008 ◽  
Author(s):  
Sebastian Cioaba ◽  
Edwin van Dam ◽  
Jack Koolen ◽  
Jae-Ho Lee
Keyword(s):  
Lower Bound ◽  
Spectral Radius

scholarly journals Compactness and Sharp Lower Bound for a 2D Smectics Model

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Michael Novack ◽  
Xiaodong Yan
Keyword(s):  
Lower Bound ◽  
Sharp Lower Bound

Success probabilities for second guessers

1980 ◽  
Vol 17 (04) ◽  
pp. 1133-1137 ◽  
Author(s):  
A. O. Pittenger
Keyword(s):  
Lower Bound ◽  
Dimensional Space ◽  
Success Probability ◽  
First Person ◽  
True Location ◽  
Rotationally Symmetric ◽  
The One ◽  
Sharp Lower Bound

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

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