Nonexistence of Efficient Dominating Sets in the Cayley Graphs Generated by Transposition Trees of Diameter 3

Italo J. Dejter; Oscar Tomaiconza

Nonexistence of Efficient Dominating Sets in the Cayley Graphs Generated by Transposition Trees of Diameter 3

Combinatorics 2021-09-28 v9

Authors: Italo J. Dejter , Oscar Tomaiconza

Abstract

Let $d,n$ be positive integers such that $d<n$ , and let $X^d_n$ be a Cayley graph generated by a transposition tree of diameter $d$ . It is known that every $X^d_n$ with $d<3$ splits into efficient dominating sets. The main result of this paper is that $X^3_n$ does not have efficient dominating sets.

Keywords

Cayley graph transposition tree efficient dominating set graph diameter graph decomposition

Cite

@article{arxiv.1703.06540,
  title  = {Nonexistence of Efficient Dominating Sets in the Cayley Graphs Generated by Transposition Trees of Diameter 3},
  author = {Italo J. Dejter and Oscar Tomaiconza},
  journal= {arXiv preprint arXiv:1703.06540},
  year   = {2021}
}

Comments

15 pages, 5 figures, 3 tables

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