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PreprintCC BY 4.0arXiv

Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property P∗

  • Swathi Shetty
  • B. R. Rakshith
  • Sayinath Udupa N. V
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Abstract

In the literature, several graph matrices based on vertex degrees have been introduced, and the study of their spectral properties has attracted considerable attention in recent years. Motivated by these developments, in this paper, we investigate the spectral radius of the weighted adjacency matrix Af(G), where the function f satisfies property P*. More precisely, we characterize the graphs that attain the maximum spectral radius of Af(G) among graphs with a vertex cut set of prescribed order, graphs with exactly s cut edges, and graphs with given vertex connectivity and independence number. Our results further develop the unified framework for studying extremal spectral properties of degree-based weighted adjacency matrices and extend this framework to several classes of graphs with prescribed structural parameters.

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Cite

BibTeXRIS
BibTeX
@misc{shetty2026extremal,
  title = {{Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property $P^\ast$}},
  author = {Swathi Shetty and B. R. Rakshith and Sayinath Udupa N. V},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30303},
  eprint = {2609.30303},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30303},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property P^∗
AU  - Swathi Shetty
AU  - B. R. Rakshith
AU  - Sayinath Udupa N. V
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.30303
UR  - https://arxiv.org/abs/2609.30303
AB  - In the literature, several graph matrices based on vertex degrees have been introduced, and the study of their spectral properties has attracted considerable attention in recent years. Motivated by these developments, in this paper, we investigate the spectral radius of the weighted adjacency matrix A_f(G), where the function f satisfies property P^*. More precisely, we characterize the graphs that attain the maximum spectral radius of A_f(G) among graphs with a vertex cut set of prescribed order, graphs with exactly s cut edges, and graphs with given vertex connectivity and independence number. Our results further develop the unified framework for studying extremal spectral properties of degree-based weighted adjacency matrices and extend this framework to several classes of graphs with prescribed structural parameters.
ER  -