TY - JOUR
T1 - On distance Laplacian spectral ordering of some graphs
AU - Rather, Bilal Ahmad
AU - Aouchiche, Mustapha
AU - Imran, Muhammad
AU - El Hallaoui, Issmail
N1 - Publisher Copyright:
© The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024.
PY - 2024/2
Y1 - 2024/2
N2 - For a connected graph G, let DL(G) be its distance Laplacian matrix (DL matrix) and ⋌1(G)≥⋌2(G)≥⋯≥⋌n-1(G)>⋌n(G)=0 be its eigenvalues. In this article, we will study the DL spectral invariants of graphs whose complements are trees. In particular, with the technique of eigenvalue/eigenvector analysis and intermediate value theorem, we order tree complements as a decreasing sequence on the basis of their second smallest DL eigenvalue ⋌n-1, the DL spectral radius ⋌1 and the DL energy. Furthermore, we will give extreme values of ⋌1(G) and of ⋌n-1(G) over a class of unicyclic graphs and their complements. We present decreasing behaviour of these graphs in terms of ⋌1(G),⋌n-1(G) and DL energy. Thereby, we obtain complete characterization of graphs minimizing/maximizing with respect to there spectral invariants over class of these unicyclic graphs.
AB - For a connected graph G, let DL(G) be its distance Laplacian matrix (DL matrix) and ⋌1(G)≥⋌2(G)≥⋯≥⋌n-1(G)>⋌n(G)=0 be its eigenvalues. In this article, we will study the DL spectral invariants of graphs whose complements are trees. In particular, with the technique of eigenvalue/eigenvector analysis and intermediate value theorem, we order tree complements as a decreasing sequence on the basis of their second smallest DL eigenvalue ⋌n-1, the DL spectral radius ⋌1 and the DL energy. Furthermore, we will give extreme values of ⋌1(G) and of ⋌n-1(G) over a class of unicyclic graphs and their complements. We present decreasing behaviour of these graphs in terms of ⋌1(G),⋌n-1(G) and DL energy. Thereby, we obtain complete characterization of graphs minimizing/maximizing with respect to there spectral invariants over class of these unicyclic graphs.
KW - 05C12
KW - 05C50
KW - 15A18
KW - Distance Laplacian energy
KW - Distance Laplacian matrix
KW - Double star
KW - Laplacian matrix
KW - Spectral invariant ordering
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U2 - 10.1007/s12190-024-01995-8
DO - 10.1007/s12190-024-01995-8
M3 - Article
AN - SCOPUS:85183193205
SN - 1598-5865
VL - 70
SP - 867
EP - 892
JO - Journal of Applied Mathematics and Computing
JF - Journal of Applied Mathematics and Computing
IS - 1
ER -