Rooted product

Rooted product --- корневое произведение.

Let [math]\displaystyle{ G = (V,E) }[/math] be a simple graph of order [math]\displaystyle{ n }[/math] and let [math]\displaystyle{ {\mathcal H} = \{H_{1}, \ldots, H_{n}\} }[/math] be a family of rooted graphs. The rooted product [math]\displaystyle{ G({\mathcal H}) }[/math] is the graph obtained by identifying the root of [math]\displaystyle{ H_{i} }[/math] with [math]\displaystyle{ i }[/math]-th vertex of [math]\displaystyle{ G }[/math]. In particular, if [math]\displaystyle{ {\mathcal H} }[/math] is the family of the paths [math]\displaystyle{ P_{k_{1}}, \ldots, P_{k_{n}} }[/math] with the rooted vertices of degree one, the corresponding graph [math]\displaystyle{ G({\mathcal H}) }[/math] is called the sunlike graph and is denoted by [math]\displaystyle{ G(k_{1}, \ldots, k_{n}) }[/math].