id: 06023643
dt: j
an: 06023643
au: Knor, M.; Potočnik, P.; Škrekovski, R.
ti: On a conjecture about Wiener index in iterated line graphs of trees.
so: Discrete Math. 312, No. 6, 1094-1105 (2012).
py: 2012
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: Wiener index; line graph; iterated line graph; tree
ci: 
li: doi:10.1016/j.disc.2011.11.023
ab: Summary: Let $G$ be a graph. Denote by $L^{i}(G)$ its i-iterated line graph
    and denote by $W(G)$ its Wiener index. Dobrynin and Melnikov
    conjectured that there exists no nontrivial tree $T$ and $i\geq 3$,
    such that $W(L^{i}(T))=W(T)$. We prove this conjecture for trees which
    are not homeomorphic to the claw $K_{1,3}$ and $H$, where $H$ is a tree
    consisting of 6 vertices, 2 of which have degree 3.
rv: