{
  "abstract": "For a group $G$ and subsets $S,T \\subset G$ 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 $S \\cup \\{e\\}$. 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30327",
  "author_total": 2,
  "authors": [
    {
      "name": "Paula M. Chiapparoli"
    },
    {
      "name": "Ricardo A. Podestá"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c41pqg506aqnr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30327",
  "fulltext_url": null,
  "id": "c41pqg506aqnr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30327",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214659976",
  "pdf_url": "https://arxiv.org/pdf/2609.30327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c41pqg506aqnr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments",
  "title_text": "The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/c41pqg506aqnr",
  "venue": "arXiv",
  "versions": []
}