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Independence number, essential connectivity and the distance spectral radius of graphs

  • Shuang Ding
  • Dan Li
  • Yuanyuan Chen
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Abstract

An independent set of a graph G is a subset of VG, no two of which are adjacent. The cardinality of a maximum independent set in a graph G is called the independence number of G, denoted by alpha(G). The essential connectivity kappa'(G) of a graph G is denoted as the minimum number of vertices of G whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the n-vertex connected graphs with given independence number and essential connectivity that attain the minimum distance spectral radius, and fully characterize the corresponding extremal graphs.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026independence,
  title = {{Independence number, essential connectivity and the distance spectral radius of graphs}},
  author = {Shuang Ding and Dan Li and Yuanyuan Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37981},
  eprint = {2609.37981},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37981},
}
RIS
TY  - UNPB
TI  - Independence number, essential connectivity and the distance spectral radius of graphs
AU  - Shuang Ding
AU  - Dan Li
AU  - Yuanyuan Chen
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37981
UR  - https://arxiv.org/abs/2609.37981
AB  - An independent set of a graph G is a subset of VG, no two of which are adjacent. The cardinality of a maximum independent set in a graph G is called the independence number of G, denoted by alpha(G). The essential connectivity kappa'(G) of a graph G is denoted as the minimum number of vertices of G whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the n-vertex connected graphs with given independence number and essential connectivity that attain the minimum distance spectral radius, and fully characterize the corresponding extremal graphs.
ER  -