TY - JOUR

T1 - Reciprocal distance Laplacian spectral properties double stars and their complements

AU - Ganie, H. A.

AU - Rather, B. A.

AU - Aouchiche, M.

N1 - Publisher Copyright:
© Ganie H.A., Rather B.A., Aouchiche M., 2023.

PY - 2023/12/30

Y1 - 2023/12/30

N2 - Several matrices are associated with graphs in order to study their properties. In such a study, researchers are interested in the spectra of the matrix under consideration, therefore, the properties are called spectral properties, with reference to the matrix. One of the interesting and hard problems in the spectral study of graphs is to order the graphs based on some spectral graph invariant, like the spectral radius, the second smallest eigenvalue, the energy, etc. Due to hardness of this problem it has been considered in the literature for small classes of graphs. Here we continue this study and add some more classes of graphs which can be ordered on the basis of spectral graph invariants. In this article, we study spectral properties of trees of diameter three, called double stars, and their complements through their reciprocal distance Laplacian eigenvalues. We give ordering of these graphs based on their reciprocal distance Laplacian spectral radius, on their second smallest reciprocal distance Laplacian eigenvalue, and on their reciprocal distance Laplacian energy.

AB - Several matrices are associated with graphs in order to study their properties. In such a study, researchers are interested in the spectra of the matrix under consideration, therefore, the properties are called spectral properties, with reference to the matrix. One of the interesting and hard problems in the spectral study of graphs is to order the graphs based on some spectral graph invariant, like the spectral radius, the second smallest eigenvalue, the energy, etc. Due to hardness of this problem it has been considered in the literature for small classes of graphs. Here we continue this study and add some more classes of graphs which can be ordered on the basis of spectral graph invariants. In this article, we study spectral properties of trees of diameter three, called double stars, and their complements through their reciprocal distance Laplacian eigenvalues. We give ordering of these graphs based on their reciprocal distance Laplacian spectral radius, on their second smallest reciprocal distance Laplacian eigenvalue, and on their reciprocal distance Laplacian energy.

KW - double star

KW - energy

KW - reciprocal distance Laplacian matrix

KW - spectral ordering

UR - http://www.scopus.com/inward/record.url?scp=85181918059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85181918059&partnerID=8YFLogxK

U2 - 10.15330/cmp.15.2.576-593

DO - 10.15330/cmp.15.2.576-593

M3 - Article

AN - SCOPUS:85181918059

SN - 2075-9827

VL - 15

SP - 576

EP - 593

JO - Carpathian Mathematical Publications

JF - Carpathian Mathematical Publications

IS - 2

ER -