Characteristic polynomials of some graph bundles. II. (English) Zbl 0755.05078

Summary: [Part I, cf. Can. J. Math. 42, No. 4, 747-761 (1990).]
The characteristic polynomial of a graph \(G\) is that of its adjacency matrix, and its eigenvalues are those of its adjacency matrix. Recently, Y. Chae, J. H. Kwak and J. Lee showed a relation between the characteristic polynomial of a graph \(G\) and those of graph bundles over \(G\). In particular, the characteristic polynomial of \(G\) is a divisor of those of its covering graphs. They also gave the complete computation of the characteristic polynomials of \(K_ 2\) (or \(\overline K_ 2)\)- bundles over a graph. In this paper, we compute the characteristic polynomial of a graph bundle when its voltages lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Some applications to path- or cycle-bundles are also discussed.


05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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