The asymptotic behavior of some indices of iterated line graphs of regular graphs

Authors:
Weigen Yan;Yeong-Nan Yeh;Fuji Zhang
Affiliations:
School of Sciences, Jimei University, Xiamen 361021, China;Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan;School of Mathematical Science, Xiamen University, Xiamen 361005, China
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

In this paper, we consider the asymptotic behavior of the number of spanning trees and the Kirchhoff index of iterated line graphs and iterated para-line graphs (or clique-inserted graphs) of a regular graph G. We show that the asymptotic behavior of these indices (except the Kirchhoff index of the iterated para-line graphs) is independent of the structure of the regular graph G.