A study on random permutation graphs

Oğuz Gürerk; Ümit Işlak; Mehmet Akif Yıldız

A study on random permutation graphs

Combinatorics 2021-08-02 v2 Probability

Authors: Oğuz Gürerk , Ümit Işlak , Mehmet Akif Yıldız

Abstract

For a given permutation $\pi_n$ in $S_n$ , a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (\pi_n(i) - \pi_n (j)) < 0$ . In this paper, we study various statistics of random permutation graphs. In particular, the degree of a given node, the number of nodes with a given degree, the number of isolated vertices, and the number of cliques are analyzed. Further, explicit formulas for the probabilities of having a given number of connected components and isolated vertices are obtained.

Keywords

preferential attachment random graphs permutations

Cite

@article{arxiv.1901.06678,
  title  = {A study on random permutation graphs},
  author = {Oğuz Gürerk and Ümit Işlak and Mehmet Akif Yıldız},
  journal= {arXiv preprint arXiv:1901.06678},
  year   = {2021}
}

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21 pages, 1 figure

A study on random permutation graphs

Abstract

Keywords

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