Crown of graphs

Crown of graphs --- корона графов.

For positive integers [math]\displaystyle{ k \leq n }[/math], the crown of graphs [math]\displaystyle{ C_{n,k} }[/math] is a graph with a vertex set [math]\displaystyle{ \{a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n}\} }[/math] and an edge set [math]\displaystyle{ \{a_{i}b_{j}: \; 1 \leq i \leq n, j = i+1, i+2, \ldots, i+k\pmod{n}\} }[/math]. For any positive integer [math]\displaystyle{ \lambda }[/math], let [math]\displaystyle{ \lambda C_{n,k} }[/math] denote a multiple graph obtained from the crown [math]\displaystyle{ C_{n,k} }[/math] by replacing each edge [math]\displaystyle{ e }[/math] by [math]\displaystyle{ \lambda }[/math] edges with the same end vertices as those of [math]\displaystyle{ e }[/math]. We call [math]\displaystyle{ \lambda C_{n,k} }[/math] a multicrown.

See also

• Corona.