On the eigenvalues of closed shadow graphs

被引：0
|
作者：
Campena, Francis Joseph H. [1 ]
Lunar, Melody Mae C. [1 ]
Sung, Inseok [1 ]
机构：
[1] De La Salle Univ, Coll Sci, Dept Math & Stat, 2401 Taft Ave, Manila 1004, Metro Manila, Philippines
来源：
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY | 2022年 / 25卷 / 06期
关键词：
Distance eigenvalue; Integral graphs; Graph spectra; Graph energy; ENERGY;
D O I：
10.1080/09720529.2022.2060609
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The energy and d-energy of a graph is the sum of the absolute values of the graphs' adjacency and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study we determine the eigenvalues and d-eigenvalues of a closed shadow graph. Thus, determining also the energy and distance energy of a closed shadow graph. As a consequence, the dosed shadow graph of G is integral whenever G is integral, that is the eigenvalues of the adjacency matrix of the graph are all integers.
引用
收藏
页码：1937 / 1944
页数：8
相关论文
共 50 条
  • [1] PARTIAL SUM OF EIGENVALUES OF RANDOM GRAPHS
    Rocha, Israel
    APPLICATIONS OF MATHEMATICS, 2020, 65 (05) : 609 - 618
  • [2] THE MULTIPLICITY OF Aα-EIGENVALUES OF GRAPHS
    Xue, Jie
    Liu, Ruifang
    Yu, Guanglong
    Shu, Jinlong
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2020, 36 : 645 - 657
  • [3] Eigenvalues and clique partitions of graphs
    Zhou, Jiang
    Bu, Changjiang
    ADVANCES IN APPLIED MATHEMATICS, 2021, 129
  • [4] On the sum of the largest Aα-eigenvalues of graphs
    Lin, Zhen
    AIMS MATHEMATICS, 2022, 7 (08): : 15064 - 15074
  • [5] Eigenvalues and energy in threshold graphs
    Jacobs, David P.
    Trevisan, Vilmar
    Tura, Fernando
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 465 : 412 - 425
  • [6] Distribution of Laplacian eigenvalues of graphs
    Das, Kinkar Ch.
    Mojallal, Seyed Ahmad
    Trevisan, Vilmar
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 508 : 48 - 61
  • [7] On the sum of powers of the Aα-eigenvalues of graphs
    Lin, Zhen
    MATHEMATICAL MODELLING AND CONTROL, 2022, 2 (02): : 55 - 64
  • [8] On the eigenvalues of eccentricity matrix of graphs
    Lei, Xingyu
    Wang, Jianfeng
    Li, Guozheng
    DISCRETE APPLIED MATHEMATICS, 2021, 295 : 134 - 147
  • [9] On Laplacian eigenvalues of connected graphs
    Milovanovic, Igor Z.
    Milovanovic, Emina I.
    Glogic, Edin
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2015, 65 (02) : 529 - 535
  • [10] Degree subtraction eigenvalues and energy of graphs
    Ramane, H. S.
    Nandeesh, K. C.
    Gudodagi, G. A.
    Zhou, B.
    COMPUTER SCIENCE JOURNAL OF MOLDOVA, 2018, 26 (02) : 146 - 162
12345