English

On minimizing the Wiener index of unicyclic graphs with fixed girth and given degree sequence

Combinatorics 2024-10-29 v2

Abstract

The Wiener index of a graph is the sum of all the distances between any pair of vertices. We aim to describe graphs which minimize the Wiener index among all unicyclic graphs with fixed girth and given degree sequence. Depending on where the centroid of the graph is, we will present three candidates for the minimization, namely the greedy unicyclic graph, the cycle-centered graph and the out-greedy unicyclic graph.

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Cite

@article{arxiv.2410.04903,
  title  = {On minimizing the Wiener index of unicyclic graphs with fixed girth and given degree sequence},
  author = {Alewyn P. Burger and Valisoa R. M. Rakotonarivo},
  journal= {arXiv preprint arXiv:2410.04903},
  year   = {2024}
}

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24 pages