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arXiv · 1901.06678

A study on random permutation graphs

Oğuz Gürerk·Ümit Işlak·Mehmet Akif Yıldız
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Abstract

For a given permutation $π_n$ in $S_n$, a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (π_n(i) - π_n (j)) < 0$. 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.

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Oğuz Gürerk, Ümit Işlak, Mehmet Akif Yıldız. 2021-07-29. A study on random permutation graphs. https://arxiv.org/abs/1901.06678

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