The Kirchhoff indices and the matching numbers of unicyclic graphs
Xuli Qi, Bo Zhou, Zhibin Du
TL;DR
This paper investigates the minimum Kirchhoff index in unicyclic graphs with a fixed number of vertices and matching number, identifying the extremal graphs that achieve this minimum.
Contribution
It provides a characterization of the unicyclic graphs that minimize the Kirchhoff index given constraints on vertices and matching number.
Findings
Identified the unicyclic graphs with the minimum Kirchhoff index for given parameters.
Characterized the extremal graphs that achieve the minimum Kirchhoff index.
Enhanced understanding of resistance distances in unicyclic graphs.
Abstract
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. It found considerable applications in a variety of fields. In this paper, we determine the minimum Kirchhoff index among the unicyclic graphs with fixed number of vertices and matching number, and characterize the extremal graphs.
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Zeolite Catalysis and Synthesis