Kwak, Jin Ho; Lee, Jaeun Characteristic polynomials of some graph bundles. II. (English) Zbl 0755.05078 Linear Multilinear Algebra 32, No. 1, 61-73 (1992). 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. Cited in 2 ReviewsCited in 26 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:characteristic polynomials; graph bundles; adjacency matrix; eigenvalues; automorphism group PDF BibTeX XML Cite \textit{J. H. Kwak} and \textit{J. Lee}, Linear Multilinear Algebra 32, No. 1, 61--73 (1992; Zbl 0755.05078) Full Text: DOI OpenURL References: [1] Biggs N., Algebraic Graph Theory (1974) · Zbl 0284.05101 [2] Chae Y., Characteristic polynomials of some graph bundles (1974) [3] Cvetkovié D. M., Spectra of Graphs (1979) [4] Gross J. L., Topological Graph Theory (1987) · Zbl 0621.05013 [5] DOI: 10.1016/0012-365X(77)90131-5 · Zbl 0375.55001 [6] Hoffman K., Linear Algebra (1971) [7] Kitamura T., Math. Japonica 35 pp 225– (1990) [8] DOI: 10.4153/CJM-1990-039-3 · Zbl 0739.05042 [9] Mohar B., Europ. J. Combinatorics 9 pp 215– (1988) [10] Schwenk, A. J. 1974. ”Computing the characteristic polynomial of a graph”. Vol. 406, 153–172. New York: Springer-Verlag. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.