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PreprintCC BY-NC-ND 4.0arXiv

Laplacian Pair State Transfer on Edge Coronas

  • Akash Kalita
  • Bikash Bhattacharjya
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Abstract

Let G be a graph with edge set E(G) = {e1, …, em}, and let ℋ = (H1, …, Hm) be an m-tuple of graphs. The edge corona Gdiamondℋ is obtained from the disjoint union of G,H1,…,Hm by joining both end vertices of each edge ej to every vertex of Hj for 1≤ j≤ m. In this paper, we investigate Laplacian perfect pair state transfer and Laplacian pretty good pair state transfer on edge coronas. We establish necessary and sufficient conditions for the existence of Laplacian perfect pair state transfer. We also derive sufficient conditions for the non-existence of Laplacian perfect pair state transfer. Further, we identify conditions under which the absence of Laplacian perfect pair state transfer guarantees the existence of Laplacian pretty good pair state transfer. Additionally, we develop constructions based on Cartesian product and tensor product to obtain a few more infinite families of edge coronas admitting Laplacian pretty good pair state transfer. Finally, we investigate the existence of Laplacian pretty good pair state transfer on the edge corona of complete graphs.

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Cite

BibTeXRIS
BibTeX
@misc{kalita2026laplacian,
  title = {{Laplacian Pair State Transfer on Edge Coronas}},
  author = {Akash Kalita and Bikash Bhattacharjya},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00866},
  eprint = {2611.00866},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00866},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Laplacian Pair State Transfer on Edge Coronas
AU  - Akash Kalita
AU  - Bikash Bhattacharjya
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00866
UR  - https://arxiv.org/abs/2611.00866
AB  - Let G be a graph with edge set E(G) = {e_1, …, e_m}, and let ℋ = (H_1, …, H_m) be an m-tuple of graphs. The edge corona Gdiamondℋ is obtained from the disjoint union of G,H_1,…,H_m by joining both end vertices of each edge e_j to every vertex of H_j for 1≤ j≤ m. In this paper, we investigate Laplacian perfect pair state transfer and Laplacian pretty good pair state transfer on edge coronas. We establish necessary and sufficient conditions for the existence of Laplacian perfect pair state transfer. We also derive sufficient conditions for the non-existence of Laplacian perfect pair state transfer. Further, we identify conditions under which the absence of Laplacian perfect pair state transfer guarantees the existence of Laplacian pretty good pair state transfer. Additionally, we develop constructions based on Cartesian product and tensor product to obtain a few more infinite families of edge coronas admitting Laplacian pretty good pair state transfer. Finally, we investigate the existence of Laplacian pretty good pair state transfer on the edge corona of complete graphs.
ER  -