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2016•Science DiscoveryOpen access

Minimum Wiener Index Value and Polar Graph of Book Graphs

Fuyi Wei

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Abstract

Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.

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Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.

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Available abstract

Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.

Key concepts: Wiener index, Topological index, Lemma (botany), Mathematics, Graph, Combinatorics, Index (typography), Graph theory

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