06000779

j

06000779 Beasley, LeRoy B. Preservers of sets of undirected graphs. Congr. Numerantium 208, 55-63 (2011). 2011 Utilitas Mathematica Publishing Inc., Winnipeg EN independence number matching number of bipartite graphs vertex cover number of undirected graphs edge independence number of undirected graphs 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.