Minimizing Kirchhoff index among graphs with a given vertex bipartiteness

Jia-Bao Liu and Xiang-Feng Pan

Applied Mathematics and Computation, 2016, vol. 291, issue C, 84-88

Abstract: The resistance distance between any two vertices of a graph G is defined as the effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of the resistance distances between all the pairs of vertices in G. The vertex bipartiteness vb of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. In this paper, we characterize the graph having the minimum Kf(G) values among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1≤vb≤n−3.

Keywords: Kirchhoff index; Vertex bipartiteness; Resistance distance; Generalized join; Laplacian eigenvalues (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:84-88

DOI: 10.1016/j.amc.2016.06.017

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