id: 06000779
dt: j
an: 06000779
au: Beasley, LeRoy B.
ti: Preservers of sets of undirected graphs.
so: Congr. Numerantium 208, 55-63 (2011).
py: 2011
pu: Utilitas Mathematica Publishing Inc., Winnipeg
la: EN
cc: 
ut: independence number; matching number of bipartite graphs; vertex cover
    number of undirected graphs; edge independence number of undirected
    graphs
ci: 
li: 
ab: Summary: Let ${\Cal G}_n$ be the set of all simple loopless undirected
    graphs on $n$ vertices. Let $T$ be a linear mapping, $T:{\Cal
    G}_n\to{\Cal G}_n$ for which the independence number of $T(G)$ is the
    same as the independence number for $G$. We show that $T$ is
    necessarily a vertex permutation. Similar results are obtained for
    mappings preserving the matching number of bipartite graphs, the vertex
    cover number of undirected graphs, and the edge independence number of
    undirected graphs.
rv: