Deng, Hanyuan The Wiener index of a class of chemical graphs and their line graphs. (English) Zbl 1212.05253 J. Nat. Sci. Hunan Norm. Univ. 32, No. 3, 23-26 (2009). 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)]. Cited in 1 Document MSC: 05C90 Applications of graph theory 05C12 Distance in graphs 05C76 Graph operations (line graphs, products, etc.) Keywords:chemical graph; line graph; Wiener index; cyclomatic number Citations:Zbl 1080.05028 PDFBibTeX XMLCite \textit{H. Deng}, J. Nat. Sci. Hunan Norm. Univ. 32, No. 3, 23--26 (2009; Zbl 1212.05253)