Wiener index in iterated line graphs
نویسندگان
چکیده
For a graph G, denote by L i (G) its i-iterated line graph and denote by W (G) its Wiener index. We prove that the function W (L i (G)) is convex in variable i. Moreover, this function is strictly convex if G is different from a path, a claw K 1,3 and a cycle. As an application we prove that W (L i (T)) = W (T) for every i ≥ 3 if T is a tree in which no leaf is adjacent to a vertex of degree 2, T = K 1 and T = K 2 .
منابع مشابه
Complete solution of equation W(L3(T))=W(T) for the Wiener index of iterated line graphs of trees
Let G be a graph. The Wiener index of G, W (G), is defined as the sum of distances between all pairs of vertices of G. Denote by L i (G) its i-iterated line graph. In the talk, we will consider the equation W (L i (T)) = W (T) where T is a tree and i ≥ 1.
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