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- Title
The Kirchhoff Index of Some Combinatorial Networks.
- Authors
Liu, Jia-Bao; Pan, Xiang-Feng; Cao, Jinde; Hu, Fu-Tao
- Abstract
The Kirchhoff index Kf(G) is the sum of the effective resistance distances between all pairs of vertices in G. The hypercube Qn and the folded hypercube FQn are well known networks due to their perfect properties. The graph G∗, constructed from G, is the line graph of the subdivision graph S(G). In this paper, explicit formulae expressing the Kirchhoff index of (Qn)∗ and (FQn)∗ are found by deducing the characteristic polynomial of the Laplacian matrix of G∗ in terms of that of G.
- Subjects
COMBINATORICS; KIRCHHOFF'S theory of diffraction; HYPERCUBES; GRAPH theory; LAPLACIAN matrices; POLYNOMIALS
- Publication
Discrete Dynamics in Nature & Society, 2015, Vol 2015, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2015/340793