Geodesic
Ordering the non-starlike trees with large reverse Wiener indices
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 215-233
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The reverse Wiener index of a connected graph $G$ is defined as \[ \Lambda (G)=\frac {1}{2}n(n-1)d-W(G), \] 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 $n\ge 8$, and the $n$-vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for $n\ge 10$.
The reverse Wiener index of a connected graph $G$ is defined as \[ \Lambda (G)=\frac {1}{2}n(n-1)d-W(G), \] 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 $n\ge 8$, and the $n$-vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for $n\ge 10$.
DOI : 10.1007/s10587-012-0007-8
Classification : 05C12, 05C35, 05C90
Keywords: distance; diameter; Wiener index; reverse Wiener index; trees; starlike trees; caterpillars 
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Li, Shuxian; Zhou, Bo. Ordering the non-starlike trees with large reverse Wiener indices. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 215-233. doi: 10.1007/s10587-012-0007-8

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