Steiner Wiener Index and Line Graphs of Trees
نویسندگان
چکیده
منابع مشابه
Wiener index of iterated line graphs of trees homeomorphic to
Let G be a graph. Denote by L(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 ≥ 3 such that W (L(T )) = W (T )? In a series of five papers we solve this problem. In a previous paper we proved that W (L(T )) > W (T ) for every tree T that is not homeomorphic to a path, claw...
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The Wiener index of a graph G, denoted by W (G), is the sum of distances between all pairs of vertices in G. In this paper, we consider the relation between the Wiener index of a graph, G, and its line graph, L(G). We show that if G is of minimum degree at least two, then W (G) ≤ W (L(G)). We prove that for every non-negative integer g0, there exists g > g0, such that there are infinitely many ...
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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,...
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ژورنال
عنوان ژورنال: Discrete mathematics letters
سال: 2022
ISSN: ['2664-2557']
DOI: https://doi.org/10.47443/dml.2021.s214