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Senbagamalar, J., Babujee, J., Gutman, I. (2014). On Wiener index of graph complements. Transactions on Combinatorics, 3(2), 11-15. doi: 10.22108/toc.2014.4577
Jaisankar Senbagamalar; Jayapal Baskar Babujee; Ivan Gutman. "On Wiener index of graph complements". Transactions on Combinatorics, 3, 2, 2014, 11-15. doi: 10.22108/toc.2014.4577
Senbagamalar, J., Babujee, J., Gutman, I. (2014). 'On Wiener index of graph complements', Transactions on Combinatorics, 3(2), pp. 11-15. doi: 10.22108/toc.2014.4577
Senbagamalar, J., Babujee, J., Gutman, I. On Wiener index of graph complements. Transactions on Combinatorics, 2014; 3(2): 11-15. doi: 10.22108/toc.2014.4577

On Wiener index of graph complements

Article 2, Volume 3, Issue 2, June 2014, Page 11-15  XML PDF (292 K)
Document Type: Research Paper
DOI: 10.22108/toc.2014.4577
Authors
Jaisankar Senbagamalar1; Jayapal Baskar Babujee1; Ivan Gutman 2
1Anna University
2University of Kragujevac Kragujevac, Serbia
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)
Main Subjects
05C12 Distance in graphs; 05C75 Structural characterization of families of graphs; 05C Combinatorics: Graph theory
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