Mathematics – Combinatorics
Scientific paper
2011-03-31
Mathematics
Combinatorics
english: 9 pages; russian: 9 pages
Scientific paper
A graph of order $n>3$ is called {switching separable} if its modulo-2 sum with some complete bipartite graph on the same set of vertices is divided into two mutually independent subgraphs, each having at least two vertices. We prove the following: if removing any one or two vertices of a graph always results in a switching separable subgraph, then the graph itself is switching separable. On the other hand, for every odd order greater than 4, there is a graph that is not switching separable, but removing any vertex always results in a switching separable subgraph. We show a connection with similar facts on the separability of Boolean functions and reducibility of $n$-ary quasigroups. Keywords: two-graph, reducibility, separability, graph switching, Seidel switching, graph connectivity, $n$-ary quasigroup
No associations
LandOfFree
On a connection between the switching separability of a graph and that of its subgraphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a connection between the switching separability of a graph and that of its subgraphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a connection between the switching separability of a graph and that of its subgraphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-342782