The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments

Abstract

For a group G and subsets S,T ⊂ G we consider a family of mirror di-Cayley graphs $MX(G;S,T)$ and mirror di-Cayley sums graphs MX⁺(G;S,T), namely those with T={e}, S or S ∪ {e}. We refer to them indistinctly by MX^*(G;S,T). We can think of MX^*(G;S,T) as two copies of the Cayley (sum) graph X^*(G,S) joined by edges determined by the connection set T. Recently, in the work \textit{Isospectral Cayley graphs with even and odd spectrum}, we study the spectrum of these graphs and several isospectrality problems. Here, we compute the energy and spectral k-moments of MX^*(G;S,T) in terms of those of the underlying Cayley graphs X(G,S). Then, we study energetic problems like hypo-, order-, and hyper-energeticity of these graphs. Finally, we give conditions for the existence of equienergetic pairs of non-isomorphic MDCGs.

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BibTeX RIS

BibTeX

@misc{chiapparoli2026energy,
  title = {{The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments}},
  author = {Paula M. Chiapparoli and Ricardo A. Podestá},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30327},
  eprint = {2609.30327},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30327},
}

RIS

TY  - UNPB
TI  - The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments
AU  - Paula M. Chiapparoli
AU  - Ricardo A. Podestá
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.30327
UR  - https://arxiv.org/abs/2609.30327
AB  - For a group G and subsets S,T ⊂ G we consider a family of mirror di-Cayley graphs $MX(G;S,T)$ and mirror di-Cayley sums graphs MX^+(G;S,T), namely those with T={e}, S or S ∪ {e}. We refer to them indistinctly by MX^*(G;S,T). We can think of MX^*(G;S,T) as two copies of the Cayley (sum) graph X^*(G,S) joined by edges determined by the connection set T. Recently, in the work \textit{Isospectral Cayley graphs with even and odd spectrum}, we study the spectrum of these graphs and several isospectrality problems. Here, we compute the energy and spectral k-moments of MX^*(G;S,T) in terms of those of the underlying Cayley graphs X(G,S). Then, we study energetic problems like hypo-, order-, and hyper-energeticity of these graphs. Finally, we give conditions for the existence of equienergetic pairs of non-isomorphic MDCGs.
ER  -

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