English

Laplacian Spectra of Regular Graph Transformations

Combinatorics 2017-05-16 v1

Abstract

For any given graph G = (V,E) we define in a certain way a new graph G(x,y,z) with the vertex set V\cup E depending on parameters x,y,z from {0,1, +, -} and call graph G(x,y,z) the (x,y,z)-transformation of G. It turns out that if G is an r-regular graph, then the Laplacian polynomial of G(x,y,z) is a function of |V|, r, and the Laplacian spectrum of G. We give a complete description of this function.

Keywords

Cite

@article{arxiv.1705.05011,
  title  = {Laplacian Spectra of Regular Graph Transformations},
  author = {Aiping Deng and Alexander Kelmans and Juan Meng},
  journal= {arXiv preprint arXiv:1705.05011},
  year   = {2017}
}

Comments

27 pages, 7 figures

R2 v1 2026-06-22T19:46:36.970Z