@article {
author = {Senbagamalar, Jaisankar and Babujee, Jayapal Baskar and Gutman, Ivan},
title = {On Wiener index of graph complements},
journal = {Transactions on Combinatorics},
volume = {3},
number = {2},
pages = {11-15},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2014.4577},
abstract = {Let $G$ be an $(n,m)$-graph. We say that $G$ has property $(\ast)$ if for every pair of its adjacent vertices $x$ and $y$, there exists a vertex $z$, such that $z$ is not adjacent to either $x$ or $y$. If the graph $G$ has property $(\ast)$, then its complement $\overline G$ is connected, has diameter 2, and its Wiener index is equal to $\binom{n}{2}+m$, i.e., the Wiener index is insensitive of any other structural details of the graph $G$. We characterize numerous classes of graphs possessing property $(\ast)$, among which are trees, regular, and unicyclic graphs.},
keywords = {distance (in graphs),Wiener index,complement (of graph)},
url = {https://toc.ui.ac.ir/article_4577.html},
eprint = {https://toc.ui.ac.ir/article_4577_18cb792ce9d2084e2316d673f256f50a.pdf}
}