Upper Bound for the Diameter of a Tree in the Quantum Graph Theory

被引：0
|
作者：
Boyko, O. P. [1 ]
Martynyuk, O. M. [1 ]
Pivovarchik, V. M. [1 ]
机构：
[1] K Ushyns Kyi South Ukrainian Natl Pedag Univ, Odessa, Ukraine
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2023年 / 74卷 / 08期
关键词：
EIGENVALUES;
D O I：
10.1007/s11253-023-02128-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study two Sturm-Liouville spectral problems on an equilateral tree with continuity and Kirchhoff conditions at the internal vertices and Neumann conditions at the pendant vertices (first problem) and with Dirichlet conditions at the pendant vertices (second problem). The spectrum of each of these problems consists of infinitely many normal (isolated Fredholm) eigenvalues. It is shown that if we know the asymptotics of eigenvalues, then it is possible to estimate the diameter of a tree from above for each of these problems.
引用
收藏
页码：1165 / 1174
页数：10
相关论文
共 50 条
  • [21] Upper bound for the span of pencil graph
    Parvathi, N.
    Rani, A. Vimala
    PROCEEDINGS OF THE 10TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND ITS APPLICATIONS (NCMTA 18), 2018, 1000
  • [22] An asymptotic upper bound for graph embeddings
    Bartzos, Evangelos
    Emiris, Ioannis Z.
    Tzamos, Charalambos
    DISCRETE APPLIED MATHEMATICS, 2023, 327 : 157 - 177
  • [23] UPPER BOUND FOR POINT ARBORICITY OF A GRAPH
    MITCHEM, JA
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (01): : 300 - &
  • [24] An Asymptotically Improved Upper Bound on the Diameter of Polyhedra
    Noriyoshi Sukegawa
    Discrete & Computational Geometry, 2019, 62 : 690 - 699
  • [25] An Asymptotically Improved Upper Bound on the Diameter of Polyhedra
    Sukegawa, Noriyoshi
    DISCRETE & COMPUTATIONAL GEOMETRY, 2019, 62 (03) : 690 - 699
  • [26] On upper bound for the quantum entropy
    Hebisch, W
    Olkiewicz, R
    Zegarlinski, B
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 329 (1-3) : 89 - 96
  • [27] Quantum Adversary (Upper) Bound
    Kimmel, Shelby
    AUTOMATA, LANGUAGES, AND PROGRAMMING, ICALP 2012 PT I, 2012, 7391 : 557 - 568
  • [28] A BOUND ON THE DIAMETER OF THE BRAUER GRAPH OF A BLOCK OF A SOLVABLE GROUP
    Cossey, James
    Yang, Yong
    ISRAEL JOURNAL OF MATHEMATICS, 2022, 250 (01) : 115 - 138
  • [29] A bound on the diameter of the Brauer graph of a block of a solvable group
    James Cossey
    Yong Yang
    Israel Journal of Mathematics, 2022, 250 : 115 - 138
  • [30] Imitation Upper Confidence Bound for Bandits on a Graph
    Lupu, Andrei
    Precup, Doina
    THIRTY-SECOND AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE / THIRTIETH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE / EIGHTH AAAI SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE, 2018, : 8113 - 8114
12345