On Wiener index of graphs and their line graphs
نویسندگان
چکیده
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 graphs G of girth g, satisfying W (G) = W (L(G)). This partially answers a question raised by Dobrynin and Mel’nikov [8] and encourages us to conjecture that the answer to a stronger form of their question is affirmative.
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