kirchhoff index and degree kirchhoff index of complete multipartite graph
Ravindra B. Bapat, Masoud Karimi, Jia-Bao Liu
TL;DR
This paper derives explicit formulas for the Kirchhoff index of complete multipartite graphs using linear algebra and investigates extremal values of this index within such graphs.
Contribution
It provides explicit formulas for the Kirchhoff index of complete multipartite graphs and explores their extremal properties, advancing understanding of resistance distances in these graphs.
Findings
Explicit formulas for Kirchhoff index of complete multipartite graphs
Identification of extremal Kirchhoff index values among such graphs
Application of linear algebra methods to resistance distance calculations
Abstract
The Kirchhoff index of a graph is defined as half of the sum of all effective resistance distances between any two vertices. Assuming a complete multipartite graph G, by methods from linear algebra we explicitly formulate effective resistance distances between any two vertices of G, and its Kirchhoff index. In rest of paper we explore extremal value of Kirchhoff index for multipartite graphs
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Zeolite Catalysis and Synthesis