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PreprintCC BY 4.0arXiv

Fractional revival in complementary prisms of graphs

  • Sarojini Mohapatra
  • Hiranmoy Pal
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Abstract

The complementary prism GG̅ of a graph G is obtained from the disjoint union of G and its complement G̅ by adding an edge between each vertex a in G and its copy a' in G̅. This paper explores a general framework for studying fractional revival with respect to real symmetric matrices with a block structure. The framework is then used to show that, for a fixed state u in G orthogonal to the all-one vector, the complementary prism GG̅ exhibits fractional revival from the state [u,0]T with respect to the adjacency, Laplacian, and signless Laplacian matrices. We further characterize perfect pair state transfer in the complementary prism of a complete graph and establish the existence of perfect pair and plus state transfer in the complementary prism of a complete bipartite graph.

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Cite

BibTeXRIS
BibTeX
@misc{mohapatra2026fractional,
  title = {{Fractional revival in complementary prisms of graphs}},
  author = {Sarojini Mohapatra and Hiranmoy Pal},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12725},
  eprint = {2609.12725},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12725},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fractional revival in complementary prisms of graphs
AU  - Sarojini Mohapatra
AU  - Hiranmoy Pal
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12725
UR  - https://arxiv.org/abs/2609.12725
AB  - The complementary prism GG̅ of a graph G is obtained from the disjoint union of G and its complement G̅ by adding an edge between each vertex a in G and its copy a' in G̅. This paper explores a general framework for studying fractional revival with respect to real symmetric matrices with a block structure. The framework is then used to show that, for a fixed state u in G orthogonal to the all-one vector, the complementary prism GG̅ exhibits fractional revival from the state [u,0]^T with respect to the adjacency, Laplacian, and signless Laplacian matrices. We further characterize perfect pair state transfer in the complementary prism of a complete graph and establish the existence of perfect pair and plus state transfer in the complementary prism of a complete bipartite graph.
ER  -