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2020•Discrete Mathematics Algorithms and ApplicationsRequires access

Wiener index of unicycle graphs with given number of even degree vertices

Peter Luo, Cun‐Quan Zhang, Xiao‐Dong Zhang

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Abstract

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].

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What this paper is about

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].

Key concepts: Wiener index, Mathematics, Combinatorics, Metric dimension, Degree (music), Graph, Chordal graph, Discrete mathematics

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