What is it about?
Resistance distance was introduced by Klein and Randić as a generalisation of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.
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Why is it important?
In this article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.
Perspectives
In this article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.
Kexiang Xu
College of Science, Nanjing University of Aeronautics & Astronautics Nanjing, Jiangsu 210016, PR China
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This page is a summary of: The Kirchhoff Index of Quasi-Tree Graphs, Zeitschrift für Naturforschung A, January 2015, De Gruyter,
DOI: 10.1515/zna-2014-0230.
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