Supposing to have this graph :
library(igraph)
g <- graph.empty(n=7,directed=FALSE)
g <- add.edges(g, c(1,2,1,3,1,4,3,5,3,4,4,5,2,7,2,6))
g <- set.vertex.attribute(g, name='vert.names',index=V(g),value=LETTERS[V(g)])

You can get the k-core subgraph in this way :
coreness <- graph.coreness(g)
maxCoreness <- max(coreness)
# if you just need to know the vertices and not to build the subgraph
# you can use this variable
verticesHavingMaxCoreness <- which(coreness == maxCoreness)
kcore <- induced.subgraph(graph=g,vids=verticesHavingMaxCoreness)
plot(kcore,
vertex.label=get.vertex.attribute(kcore,name='vert.names',index=V(kcore)))
