2,689 research outputs found
The skew energy of random oriented graphs
Given a graph , let be an oriented graph of with the
orientation and skew-adjacency matrix . The skew energy
of the oriented graph , denoted by , is
defined as the sum of the absolute values of all the eigenvalues of
. In this paper, we study the skew energy of random oriented
graphs and formulate an exact estimate of the skew energy for almost all
oriented graphs by generalizing Wigner's semicircle law. Moreover, we consider
the skew energy of random regular oriented graphs , and get an
exact estimate of the skew energy for almost all regular oriented graphs.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1011.6646 by
other author
Switching Reconstruction of Digraphs
Switching about a vertex in a digraph means to reverse the direction of every
edge incident with that vertex. Bondy and Mercier introduced the problem of
whether a digraph can be reconstructed up to isomorphism from the multiset of
isomorphism types of digraphs obtained by switching about each vertex. Since
the largest known non-reconstructible oriented graphs have 8 vertices, it is
natural to ask whether there are any larger non-reconstructible graphs. In this
paper we continue the investigation of this question. We find that there are
exactly 44 non-reconstructible oriented graphs whose underlying undirected
graphs have maximum degree at most 2. We also determine the full set of
switching-stable oriented graphs, which are those graphs for which all
switchings return a digraph isomorphic to the original
- β¦