1
$\begingroup$

Consider the graph we get by taking the complete graph on $n$ vertices, and then attaching a pendant vertex to each of the $n$ vertices by an edge. Does such a graph have a name, i.e. do such graphs appear somewhere in the literature? Informally, this is like the star graph, but the center is not a single vertex, but a clique.

For example, such graphs are split graphs, but not every split graph is such a graph, so this is not sufficient.

$\endgroup$
3
$\begingroup$

This would be the corona of $K_n$ and $K_1$, usually denoted $K_n \circ K_1$.

The original definition was by Harary and Frucht in 1970 in their paper "On the Corona of Two Graphs"

See this question for an application of it to more general graphs: Eccentricity in corona product

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.