Lower bound on the distance $k$-domination number of a tree

Joanna Raczek; Magdalena Lemańska; Joanna Cyman

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Ordering the non-starlike trees with large reverse Wiener indices

Shuxian Li, Bo Zhou (2012)

Czechoslovak Mathematical Journal

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The reverse Wiener index of a connected graph $G$ is defined as $Λ (G) = \frac{1}{2} n (n - 1) d - W (G),$ where $n$ is the number of vertices, $d$ is the diameter, and $W (G)$ is the Wiener index (the sum of distances between all unordered pairs of vertices) of $G$ . We determine the $n$ -vertex non-starlike trees with the first four largest reverse Wiener indices for $n \geq 8$ , and the $n$ -vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for $n \geq 10$ .