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2009•Hu'nan Shifan Daxue xuebao. Ziran kexue banRequires access

The Wiener Index of a Class of Chemical Graphs and Their Line Graphs

Hanyuan Deng

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Wiener index, Combinatorics, Mathematics, Bipartite graph, Indifference graph, Chordal graph, 1-planar graph, Topological index

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