• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.1045-1067
• /
• 2022

Given a graph G, a {1, 3, …, 2n-1}-factor of G is a spanning subgraph of G, in which each degree of vertices is one of {1, 3, …, 2n-1}, where n is a positive integer. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {1, 3, …, 2n-1}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {1, 3, …, 2n-1}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.

• Kyungpook Mathematical Journal
• /
• v.54 no.3
• /
• pp.425-441
• /
• 2014

In this paper, we first present the properties of the graph which maximize the spectral radius among all graphs with prescribed degree sequence. Using these results, we provide a somewhat simpler method to determine the unicyclic graph with maximum spectral radius among all unicyclic graphs with a given degree sequence. Moreover, we determine the bicyclic graph which has maximum spectral radius among all bicyclic graphs with a given degree sequence.

• East Asian mathematical journal
• /
• v.37 no.3
• /
• pp.295-305
• /
• 2021

In this paper, we analyze the efficiency of a domain decomposition method for the two-dimensional telegraph equations. We formulate the theoretical spectral radius of the iteration matrix generated by the domain decomposition method, because the rate of convergence of an iterative algorithm depends on the spectral radius of the iteration matrix. The theoretical spectral radius is confirmed by the experimental one using MATLAB. Speedup and operation ratio of the domain decomposition method are also compared as the two measurements of the efficiency of the method. Numerical results support the high efficiency of the domain decomposition method.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.109-116
• /
• 2010

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.123-131
• /
• 2009

In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.

• International Journal of Precision Engineering and Manufacturing
• /
• v.7 no.1
• /
• pp.9-12
• /
• 2006

A spectral analysis and numerical simulation are employed to assess the effects of the stylus tip radius on measuring surface profiles. Original profiles with fractal spectral densities are generated and then are numerically traced with circular tipped stylus. Instead of their spectral densities, the accumulative power spectrums of traced profiles are analyzed. It is shown that the minimum wavelength of traced profile relates directly to the radius r of the stylus tip and the root-mean-square (rms) roughness ${\sigma}_o$ of original profile. From this accumulation spectral analysis, a formula is developed to estimate the minimum wavelength of traced profile. By using the concept of the minimum wavelength, an appropriate stylus tip radius can be chosen for the given rms roughness ${\sigma}_o$ of the profile.

• Journal of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.941-953
• /
• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.299-308
• /
• 1997

In this paper we show that the limit of a convergent in-vertible sequence in the set of invertible elements Inv(A) in a Banach algebra A under a certain conditions is invertible and we investigate some properties of the spectral radius of banach algebra with unit.

• Journal of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.959-986
• /
• 2023

Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ${\rho}(G){\leq}{\sqrt{{\lfloor}{\frac{n^2}{4}}{\rfloor}}}$, and equality holds if and only if G is $K_{{\lceil}{\frac{n}{2}}{\rceil},{\lfloor}{\frac{n}{2}}{\rfloor}}$. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.583-590
• /
• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.