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From Wheel to Jahangir graphs: spectra and energy under structured edge deletion

  • Diego Bravo
  • Florencia Cubría
  • Annabella Zapattini
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Abstract

The energy of a graph, introduced by Gutman, is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In this work we study how the energy of the Wheel graph Wn changes when a specific set of spokes is removed. The resulting graphs are precisely the Jahangir graphs Jm,n, where m divides n, and which may also be viewed as the Cycle graph Cn together with an additional vertex adjacent to certain vertices of Cn in a cyclic pattern. We determine the spectra of J2,n, J4,n, and J6,n by exploiting a factorization of their characteristic polynomials arising from equitable partitions. This yields explicit closed formulas for their energies. Moreover, under certain conditions, we establish the following monotonicity chain: ℰ(Cn) ≤ ℰ(J6,n) ≤ ℰ(J4,n) ≤ ℰ(J2,n) ≤ ℰ(Wn).

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Cite

BibTeXRIS
BibTeX
@misc{bravo2026from,
  title = {{From Wheel to Jahangir graphs: spectra and energy under structured edge deletion}},
  author = {Diego Bravo and Florencia Cubría and Annabella Zapattini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28861},
  eprint = {2610.28861},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28861},
}
RIS
TY  - UNPB
TI  - From Wheel to Jahangir graphs: spectra and energy under structured edge deletion
AU  - Diego Bravo
AU  - Florencia Cubría
AU  - Annabella Zapattini
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28861
UR  - https://arxiv.org/abs/2610.28861
AB  - The energy of a graph, introduced by Gutman, is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In this work we study how the energy of the Wheel graph W_n changes when a specific set of spokes is removed. The resulting graphs are precisely the Jahangir graphs J_m,n, where m divides n, and which may also be viewed as the Cycle graph C_n together with an additional vertex adjacent to certain vertices of C_n in a cyclic pattern. We determine the spectra of J_2,n, J_4,n, and J_6,n by exploiting a factorization of their characteristic polynomials arising from equitable partitions. This yields explicit closed formulas for their energies. Moreover, under certain conditions, we establish the following monotonicity chain: ℰ(C_n) ≤ ℰ(J_6,n) ≤ ℰ(J_4,n) ≤ ℰ(J_2,n) ≤ ℰ(W_n).
ER  -