A Sharp Lower Bound on the Least Signless Laplacian Eigenvalue of a Graph

2016 ◽  
Vol 41 (4) ◽  
pp. 2011-2018 ◽  
Author(s):  
Xiaodan Chen ◽  
Yaoping Hou
Keyword(s):  
Lower Bound ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Sharp Lower Bound

scholarly journals A sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets

2018 ◽  
Vol 6 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Milica Andeelić ◽  
Domingos M. Cardoso ◽  
António Pereira
Keyword(s):  
Lower Bound ◽  
Perfect Matching ◽  
Computational Experiments ◽  
Sufficient Condition ◽  
Hamiltonian Graphs ◽  
Laplacian Spectra ◽  
Signless Laplacian ◽  
Regular Sets ◽  
Sharp Lower Bound ◽  
Better Than

Abstract A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching. Furthermore, computational experiments revealed that the introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).

scholarly journals A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph

2008 ◽  
Vol 429 (11-12) ◽  
pp. 2770-2780 ◽  
Author(s):  
Domingos M. Cardoso ◽  
Dragoš Cvetković ◽  
Peter Rowlinson ◽  
Slobodan K. Simić
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Least Eigenvalue ◽  
Signless Laplacian ◽  
Sharp Lower Bound

scholarly journals A lower bound on the least signless Laplacian eigenvalue of a graph

2014 ◽  
Vol 448 ◽  
pp. 217-221 ◽  
Author(s):  
Shu-Guang Guo ◽  
Yong-Gao Chen ◽  
Guanglong Yu
Keyword(s):  
Lower Bound ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian

Signless Laplacian spectral characterization of some joins

2015 ◽  
Vol 30 ◽  
Author(s):  
Xiaogang Liu ◽  
Pengli Lu
Keyword(s):  
Lower Bound ◽  
Characteristic Polynomial ◽  
Regular Graph ◽  
Spectral Characterization ◽  
Laplacian Eigenvalue ◽  
Laplacian Spectra ◽  
Signless Laplacian

The join of two disjoint graphs G and H, denoted by G ∨ H, is the graph obtained by joining each vertex of G to each vertex of H. In this paper, the signless Laplacian characteristic polynomial of the join of two graphs is first formulated. And then, a lower bound for the i-th largest signless Laplacian eigenvalue of a graph is given. Finally, it is proved that G ∨ K_m, where G is an (n − 2)-regular graph on n vertices, and K_n ∨ K_2 except for n = 3, are determined by their signless Laplacian spectra.

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 On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

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
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