منابع مشابه
Weighted Zeta Functions of Graph Coverings
We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.
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Graphs and digraphs treated here are finite and simple. Let G be a connected graph and D the symmetric digraph corresponding to G. A path P of length n in D(G) is a sequence P=(v0 , v1 , ..., vn&1 , vn) of n+1 vertices and n arcs (edges) such that consecutive vertices share an arc (edge) (we do not require that all vertices are distinct). Also, P is called a (v0 , vn)-path. The subdigraph (subg...
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We define a weighted zeta function of a digraph and a weighted L-function of a symmetric digraph, and give determinant expressions of them. Furthermore, we give a decomposition formula for the weighted zeta function of a g-cyclic -cover of a symmetric digraph for any finite group and g ∈ . A decomposition formula for the weighted zeta function of an oriented line graph L(G̃) of a regular coverin...
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We consider the (Ihara) zeta functions of line graphs, middle graphs and total graphs of a regular graph and their (regular or irregular) covering graphs. Let L(G), M(G) and T (G) denote the line, middle and total graph of G, respectively. We show that the line, middle and total graph of a (regular and irregular, respectively) covering of a graph G is a (regular and irregular, respectively) cov...
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Graphs and digraphs treated here are finite and simple. Let G = (V (G), E(G)) be a connected graph with vertex set V (G) and edge set E(G), and D the symmetric digraph corresponding toG. SetD(G) = {(u, v), (v, u) | uv ∈ E(G)}. For e = (u, v) ∈ D(G), set u = o(e) and v = t(e). Furthermore, let e−1 = (v, u) be the inverse of e = (u, v). A path P of length n in G is a sequence P = (e1, · · · , en)...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1117