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PreprintCC BY 4.0arXiv

The Distance Laplacian and Distance Signless Laplacian Spectra of 𝒞-Graphs

  • Santanu Mandal
  • Pallabi Manna
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Abstract

Mandal and Mehatari (\emph{Comp.\ Appl.\ Math.}, 2025) introduced the class 𝒞 of cographs generated by a finite creation sequence (α1,…,αm) of natural numbers, and derived the inertia, an extended eigenvalue-free interval, and the exact characteristic polynomial for the \emph{adjacency} matrix of such graphs. In this note we develop the parallel theory for the \emph{distance Laplacian} matrix DL(G) and \emph{distance signless Laplacian} matrix DQ(G). It is shown that (0,αmin) ∪ (n−αmin, n), (0,n) ∪ (n, n+αmin) ∪ (2n−αmin, 2n), (2Trmin, μmax(DQ(G))) are the eigenvalue-free intervals of the Laplacian, distance Laplacian, and distance signless Laplacian matrices respectively for the said class of graphs.

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Cite

BibTeXRIS
BibTeX
@misc{mandal2026distance,
  title = {{The Distance Laplacian and Distance Signless Laplacian Spectra of $\mathcalC$-Graphs}},
  author = {Santanu Mandal and Pallabi Manna},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08599},
  eprint = {2610.08599},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08599},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Distance Laplacian and Distance Signless Laplacian Spectra of 𝒞-Graphs
AU  - Santanu Mandal
AU  - Pallabi Manna
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08599
UR  - https://arxiv.org/abs/2610.08599
AB  - Mandal and Mehatari (\emph{Comp.\ Appl.\ Math.}, 2025) introduced the class 𝒞 of cographs generated by a finite creation sequence (α_1,…,α_m) of natural numbers, and derived the inertia, an extended eigenvalue-free interval, and the exact characteristic polynomial for the \emph{adjacency} matrix of such graphs. In this note we develop the parallel theory for the \emph{distance Laplacian} matrix D^L(G) and \emph{distance signless Laplacian} matrix D^Q(G). It is shown that (0,α_min) ∪ (n−α_min, n), (0,n) ∪ (n, n+α_min) ∪ (2n−α_min, 2n), (2Tr_min, μ_max(D^Q(G))) are the eigenvalue-free intervals of the Laplacian, distance Laplacian, and distance signless Laplacian matrices respectively for the said class of graphs.
ER  -