A generalized Bartholdi zeta function for a regular covering of a bipartite graph
نویسندگان
چکیده
منابع مشابه
A New Bartholdi Zeta Function of a Graph
We define a new type of the Bartholdi zeta function of a graph G, and give a determinant expression of it. Furthermore, we define a new type of the Bartholdi L-function of G, and present a determinant expression for a new type of the Bartholdi L-function of G. As a corollary, we show that a new type of the Bartholdi zeta function of a regular covering of G is a product of new Batholdi L-functio...
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As a continuation of computing the Bartholdi zeta function of a regular covering of a graph by Mizuno and Sato in J. Combin. Theory Ser. B 89 (2003) 27, we derive in this paper some computational formulae for the Bartholdi zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the fiber is a Schreier graph or it is regular and the voltages to derive the bundl...
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We consider the weighted Bartholdi zeta function of a digraph D, and give a new determinant expression of it. Furthermore, we treat a weighted L-function of D, and give a new determinant expression of it. As a corollary, we present determinant expressions for the Bartholdi edge zeta functions of a graph and a digraph.
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Recently, Storm [8] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi...
متن کاملCovering a bipartite graph with cycles passing through given edges
We propose a conjecture: for each integer k 2:: 2, there exists N (k) such that if G = (Vb \12; E) is a bipartite graph with IV11 = 1\121 = n 2: N(k) and d( x) + d(y) 2: n + k for each pair of non-adjacent vertices x and y of G with x E V1 and y E \12, then for any k independent edges el, ... , ek of G, there exist k vertex-disjoint cycles G1, ... , Gk in G such that ei E E(Gi ) for all i E {I,...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.09.007