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ZETA FUNCTIONS OF GRAPH BUNDLES
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 Title & Authors
ZETA FUNCTIONS OF GRAPH BUNDLES
Feng, Rongquan; Kwak, Jin-Ho;
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 Abstract
As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.
 Keywords
zeta function;graph bundle;voltage assignment;discrete torus or Klein bottle;
 Language
English
 Cited by
1.
Bartholdi zeta and L-functions of weighted digraphs, their coverings and products, Advances in Mathematics, 2007, 213, 2, 865  crossref(new windwow)
2.
Zeta functions of infinite graph bundles, Linear and Multilinear Algebra, 2010, 58, 2, 185  crossref(new windwow)
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