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 = {161-175},
ISSN = {1234-3099},
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.},