Wiener index of unicycle graphs with given number of even degree vertices-Reference-Cited by-同舟云学术

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

Published:2020-05-28 Issue:04 Volume:12 Page:2050054
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Luo Peter¹,Zhang Cun-Quan²,Zhang Xiao-Dong³

Affiliation:

1. Morgantown High School, Morgantown, WV 26501, USA

2. Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA

3. School of Mathematical Sciences, MOE-LSC, SHL-MAC, Shanghai Jiao Tong University, Shanghai, P. R. China

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].

Funder

Major Research Plan

Key Programme

The montenegin-Chinese Science and Technology Cooperation Project

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830920500548

Reference22 articles.

1. Distance and Eccentric sequences to bound the Wiener index, Hosoya polynomial and the average eccentricity in the strong products of graphs

2. Total Distance, Wiener Index and Opportunity Index in Wreath Products of Star Graphs

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