Maximizing Kirchhoff index of unicyclic graphs with fixed maximum degree
Dong Li, Xiang-Feng Pan, Jia-Bao Liu, Hui-Qing Liu
TL;DR
This paper identifies the unicyclic graphs with a fixed number of vertices and maximum degree that maximize the Kirchhoff index, providing a clear characterization of the extremal graph.
Contribution
It determines the maximum Kirchhoff index for unicyclic graphs with given parameters and characterizes the extremal graph achieving this maximum.
Findings
Maximum Kirchhoff index among unicyclic graphs with fixed parameters identified.
Extremal graph characterized explicitly.
Results applicable to network analysis and graph theory.
Abstract
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Advanced Battery Materials and Technologies