  Let $G$ be a graph, $H$ be a subgraph of $G$, and let $G- H$ be the graph
obtained from $G$ by removing a copy of $H$. Let $K_{1, n}$ be the star on $n+
1$ vertices. Let $t\geq 2$ be an integer and $H_{1}, \dots, H_{t}$ and $H$ be
graphs, and let $H\rightarrow (H_{1}, \dots, H_{t})$ denote that every $t$
coloring of $E(H)$ yields a monochromatic copy of $H_{i}$ in color $i$ for some
$i\in [t]$. Ramsey number $r(H_{1}, \dots, H_{t})$ is the minimum integer $N$
such that $K_{N}\rightarrow (H_{1}, \dots, H_{t})$. Star-critical Ramsey number
$r_{*}(H_{1}, \dots, H_{t})$ is the minimum integer $k$ such that $K_{N}- K_{1,
N- 1- k}\rightarrow (H_{1}, \dots, H_{t})$ where $N= r(H_{1}, \dots, H_{t})$.
Let $rr(H_{1}, \dots, H_{t})$ be the regular Ramsey number for $H_{1}, \dots,
H_{t}$, which is the minimum integer $r$ such that if $G$ is an $r$-regular
graph on $r(H_{1}, \dots, H_{t})$ vertices, then $G\rightarrow (H_{1}, \dots,
H_{t})$. Let $m_{1}, \dots, m_{t}$ be integers larger than one, exactly $k$ of
which are even. In this paper, we prove that if $k\geq 2$ is even, then
$r_{*}(K_{1, m_{1}}, \dots, K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t+ 1-
\frac{k}{2}$ which disproves a conjecture of Budden and DeJonge in 2022.
Furthermore, we prove that if $k\geq 2$ is even, then $rr(K_{1, m_{1}}, \dots,
K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t$. Otherwise, $rr(K_{1, m_{1}}, \dots,
K_{1, m_{t}})= \sum_{i= 1}^{t} m_{i}- t+ 1$.
