@article{, AUTHOR = {Dobrynin, Andrey A. and Mel'nikov, Leonid S.}, TITLE = {Wiener index of generalized stars and their quadratic line graphs}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {26}, YEAR = {2006}, NUMBER = {1}, PAGES = {161175}, ISSN = {12343099}, ABSTRACT = {The Wiener index, $W$, is the sum of distances between all pairs of vertices
in a graph $G$. The quadratic line graph is defined as $L(L(G))$, where $L(G)$
is the line graph of $G$. A generalized star $S$ is a tree consisting of
$\Delta\geq 3$ paths with the unique common endvertex. A relation between
the Wiener index of $S$ and of its quadratic graph is presented. It is shown
that generalized stars having the property $W(S)=W(L(L(S))$ exist only for
$4\leq\Delta\leq 6$. Infinite families of generalized stars with this property
are constructed.}, }
