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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 1

On the Wiener index of unicyclic graphs

Yi HONG
Huiqing LIU
Xiaoying WU
Pages
63–68
Publication Date
2022-10-18
DOI
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⚡ TL;DR(Too Long; Didn't Read)

In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.

📌 3 Key Takeaways

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Objective & Hypothesis:The Wiener index of a graph G is defined as W(G) = $Sigma _{u,v} d_G (u, v),$ where $ d_G (u, v)$ is the distance between u and v in G, and the sum goes over all pairs of vertices.
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Key Findings & Data:The Wiener index of a graph G is defined as W(G) = $Sigma _{u,v} d_G (u, v),$ where $ d_G (u, v)$ is the distance between u and v in G, and the sum goes over all pairs of vertices.
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Conclusion & Impact:In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The Wiener index of a graph G is defined as W(G) = $Sigma _{u,v} d_G (u, v),$ where $ d_G (u, v)$ is the distance between u and v in G, and the sum goes over all pairs of vertices. In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.

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Cite This Article

HONG, Y., LIU, H., WU, X. (2022). On the Wiener index of unicyclic graphs. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 1, 63–68. https://ajindex.com/articles/530555

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