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The Wiener index of a class of chemical graphs and their line graphs. (English) Zbl 1212.05253

Summary: The Wiener index \(W(G)\) of a graph \(G=(V, E)\) is a distance-based topological index defined as the sum of distances between all pairs of vertices in \(G\). For any integer \(n\), an infinite family of planar and bipartite chemical graphs with cyclomatic number two are constructed such that their line graphs are also chemical graphs, and the difference of the Wiener indices between the graphs and their line graphs is \(n\). This affirms partly an open problem proposed by A. D. Dobrynin and L. S. Mel’nikov [MATCH Commun. Math. Comput. Chem. 53, No.1, 209–214 (2005; Zbl 1080.05028)].

MSC:

05C90 Applications of graph theory
05C12 Distance in graphs
05C76 Graph operations (line graphs, products, etc.)

Citations:

Zbl 1080.05028
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