On the minimum Kirchhoff index of graphs with a given vertex k-partiteness and edge k-partiteness

Weihua He, Hao Li and Shuofa Xiao

Applied Mathematics and Computation, 2017, vol. 315, issue C, 313-318

Abstract: The Kirchhoff index of a connected graph is the sum of the resistance distance between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. The vertex (resp. edge) k-partiteness of a graph G with n vertices is the minimum number of vertices (resp. edges) whose deletion from G yields a k-partite graph. In this paper, we determine the minimum Kirchhoff index of graphs with a given vertex k-partiteness and the minimum Kirchhoff index of graphs with a given edge bipartiteness, when the given edge bipartiteness is no more than n4.

Keywords: Kirchhoff index; Vertex k-partiteness; Edge k-partiteness; Resistance distance (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:315:y:2017:i:c:p:313-318

DOI: 10.1016/j.amc.2017.07.067

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