论文标题
关于互补棱镜的单声音凸度
On the monophonic convexity in complementary prisms
论文作者
论文摘要
如果$ s $包含所有属于$ s $的两个顶点的所有诱导路径的所有顶点，则图$ g $的$ s $是$ g $的顶点。 $ g $的最大正确单声音凸的基数称为$ g $的\ emph {单声音凸数}。 $ g $的$ s $的$ s $的\ emph {单声音间隔}是$ g $的$ s $是套件$ s $，每个顶点属于任何诱导的路径，连接两个$ s $的顶点。最低集合$ s \ subseteq v（g）$的基数为$ v（g）$，称为$ g $的\ emph {nonophonic number}。 $ g $的$ s $顶点的\ emph {单声音凸壳}是$ g $中包含$ s $的最小的单声音凸套装。最低集合$ s \ subseteq v（g）$的基数为$ v（g）$，称为$ g $的\ emph {nonophonic hull number}。 \ emph {互补的prism} $ \ gg $ $ g $的$ gg $是从$ g $的不相交联合及其补充$ \ overline {g} $获得的，通过添加它们之间的完美匹配的边缘。在这项工作中，我们确定了所有图的单声音凸数，单声音数和互补棱镜的单声音船体数。
A set $S$ of vertices of a graph $G$ is \emph{monophonic convex} if $S$ contains all the vertices belonging to any induced path connecting two vertices of $S$. The cardinality of a maximum proper monophonic convex set of $G$ is called the \emph{monophonic convexity number} of $G$. The \emph{monophonic interval} of a set $S$ of vertices of $G$ is the set $S$ together with every vertex belonging to any induced path connecting two vertices of $S$. The cardinality of a minimum set $S \subseteq V(G)$ whose monophonic interval is $V(G)$ is called the \emph{monophonic number} of $G$. The \emph{monophonic convex hull} of a set $S$ of vertices of $G$ is the smallest monophonic convex set containing $S$ in $G$. The cardinality of a minimum set $S \subseteq V(G)$ whose monophonic convex hull is $V(G)$ is called the \emph{monophonic hull number} of $G$. The \emph{complementary prism} $\GG$ of $G$ is obtained from the disjoint union of $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between them. In this work, we determine the monophonic convexity number, the monophonic number, and the monophonic hull number of the complementary prisms of all graphs.
