Wiener index of iterated line graphs of trees homeomorphic to the claw K sub {1,3} - Knor, Martin (Ars mathematica contemporanea, 2013)
Let ?$G$? be a graph. Denote by ?$L^i(G)$? its ?$i$?-iterated line graph and denote by ?$W(G)$? its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree ?$T$? and ?$i \ge 3$? such that ?$W(L^i(T)) = W(T)$?? In a series of five papers we solve this problem. In a previous paper we proved that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? that is not homeomorphic to a path, claw ?$K_{1,3}$? and to the graph of "letter ?$H$?", where ?$i \ge 3$?. Here we prove that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? homeomorphic to the claw, ?$T \ne K_{1,3}$? and ?$i \ge 4$?.
Keywords: claw; drevo; graph theory; line graph; povezavni graf; teorija grafov; tree; Wiener index; Wienerjev indeks