The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs

Authors:
Weizhong Wang;Dong Yang;Yanfeng Luo
Affiliations:
-;-;-
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 6
Cited 0

Topics in matrix analysis

Topics in matrix analysis
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SIAM Journal on Matrix Analysis and Applications
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Kirchhoff index of composite graphs

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Kirchhoff index in line, subdivision and total graphs of a regular graph

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Abstract

Let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge, and Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. In this paper, we determine the Laplacian polynomials of R(G) and Q(G) of a regular graph G; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs.