2 problems

Let $G$ be a connected graph, and let $u$ and $v$ be adjacent vertices of $G$ with degree at least $2$. Let $G_{p,q}(u,v)$ denote the graph obtained by attaching pendent paths of l…

Let $G$ be a connected graph, let $u$ be a vertex of $G$, and let $G_{p,q}(u)$ denote the graph obtained by attaching pendent paths of lengths $p$ and $q$ at $u$. For…