on wiener index of graph complements
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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 $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis 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.
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Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume 3
issue 2 2014
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