On the Local and Global Mean Orders of Sub-$k$-Trees of $k$-Trees
On the Local and Global Mean Orders of Sub-$k$-Trees of $k$-Trees
In this paper we show that for a given $k$-tree $T$ with a $k$-clique $C$, the local mean order of all sub-$k$-trees of $T$ containing $C$ is not less than the global mean order of all sub-$k$-trees of $T$, and the path-type $k$-trees have the smallest global mean sub-$k$-tree order …