Ordering the non-starlike trees with large reverse Wiener indices

Shuxian Li; Bo Zhou

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 1, page 215-233
  • ISSN: 0011-4642

Abstract

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The reverse Wiener index of a connected graph G is defined as Λ ( G ) = 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 ≥ 8 , and the n -vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for n ≥ 10 .

How to cite

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Li, Shuxian, and Zhou, Bo. "Ordering the non-starlike trees with large reverse Wiener indices." Czechoslovak Mathematical Journal 62.1 (2012): 215-233. <http://eudml.org/doc/246631>.

@article{Li2012,
abstract = {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 $n\ge 10$.},
author = {Li, Shuxian, Zhou, Bo},
journal = {Czechoslovak Mathematical Journal},
keywords = {distance; diameter; Wiener index; reverse Wiener index; trees; starlike trees; caterpillars; diameter; Wiener index; reverse Wiener index; tree},
language = {eng},
number = {1},
pages = {215-233},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ordering the non-starlike trees with large reverse Wiener indices},
url = {http://eudml.org/doc/246631},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Li, Shuxian
AU - Zhou, Bo
TI - Ordering the non-starlike trees with large reverse Wiener indices
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 215
EP - 233
AB - 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 $n\ge 10$.
LA - eng
KW - distance; diameter; Wiener index; reverse Wiener index; trees; starlike trees; caterpillars; diameter; Wiener index; reverse Wiener index; tree
UR - http://eudml.org/doc/246631
ER -

References

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