论文标题
旋塞图上的几个罗马统治图形不变性
Several Roman domination graph invariants on Kneser graphs
论文作者
论文摘要
本文考虑了以下三个罗马统治图在旋塞图上不变的图： 罗马统治，罗马全统治和签署的罗马统治。 对于kneser图$ k_ {n，k} $，我们提出了罗马统治数字$γ_{r}（k_ {n，k}）$的确切值和总罗马统治号码$γ_{tr}（k_ {k_ {n，k}）$，证明了$ n \ n \ geqslant k（k+geqslant k+1）$，k+1） =γ_{tr}（k_ {n，k}）= 2（k+1）$。 For signed Roman domination number $γ_{sR}(K_{n,k})$, the new lower and upper bounds for $K_{n,2}$ are provided: we prove that for $n\geqslant 12$, the lower bound is equal to 2, while the upper bound depends on the parity of $n$ and is equal to 3 if $n$ is odd, and equal to $5$ if $n$ is even.对于较小维度的图，可以通过应用文献中的精确方法找到精确的值。
This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination. For Kneser graph $K_{n,k}$, we present exact values for Roman domination number $γ_{R}(K_{n,k})$ and total Roman domination number $γ_{tR}(K_{n,k})$ proving that for $n\geqslant k(k+1)$, $γ_{R}(K_{n,k}) =γ_{tR}(K_{n,k}) = 2(k+1)$. For signed Roman domination number $γ_{sR}(K_{n,k})$, the new lower and upper bounds for $K_{n,2}$ are provided: we prove that for $n\geqslant 12$, the lower bound is equal to 2, while the upper bound depends on the parity of $n$ and is equal to 3 if $n$ is odd, and equal to $5$ if $n$ is even. For graphs of smaller dimensions, exact values are found by applying exact methods from literature.
