Hirobumi Mizuno

Optical orthogonal codes obtained from conics on finite projective planes

Optical orthogonal codes can be applied to fiber optical code division multiple access (CDMA) communications. In this paper, we show that optical orthogonal codes with auto- and cross-correlations at most 2 can be obtained from conics on a finite projective plane. In addition, the obtained codes asymptotically attain the upper bound on the number of codewords when the order q of the base field is large enough.

Zeta Functions of Graph Coverings

Abstract We give a decomposition formula for the zeta function of a group covering of a graph.

Bartholdi zeta functions of graph coverings

We give a decomposition formula for the Bartholdi zeta function of a regular covering of a graph G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of a regular covering of G by L-functions of G. Also, we present another proof of the determinant expression of the L-function of G.

Zeta functions of digraphs

Abstract We define a zeta function of a digraph and an L -function of a symmetric digraph, and give determinant expressions of them. Furthermore, we give a decomposition formula for the zeta function of a g -cyclic Γ -cover of a symmetric digraph for any finite group Γ and g∈Γ .

Weighted zeta functions of graphs

We give a decomposition formula for the weighted zeta function of a regular covering of a graph.

On the weighted complexity of a regular covering of a graph

We consider the weighted complexity of a graph G, and present a generalization of Northshields Theorem on the complexity of G. Furthermore, we give an explicit formula for the weighted complexity of a regular covering H of G in terms of that of G and a product of determinants over the all distinct irreducible representations of the covering transformation group of H.

Bartholdi zeta functions of digraphs

We give a determinant expression for the Bartholdi zeta function of a digraph which is not symmetric. This is a generalization of Bartholdis result on the Bartholdi zeta function of a graph or a symmetric digraph.

Weighted zeta functions of digraphs

Abstract 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 Γ -cover of a symmetric digraph for any finite group Γ and g ∈ Γ . A decomposition formula for the weighted zeta function of an oriented line graph L → ( G ) of a regular covering G of a graph G is given. Furthermore, we define a weighted L -function of an oriented line graph L → (G) of G , and present a factorization formula for the weighted zeta function of L → ( G ) by weighted L -functions of L → (G) . As a corollay, we obtain a factorization formula for the multiedge zeta function of G given by Stark and Terras.

Bartholdi zeta functions of some graphs

We give a decomposition formula for the Bartholdi zeta function of a graph G which is partitioned into some irregular coverings. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of G which is partitioned into some regular coverings.

The semicircle law for semiregular bipartite graphs

We give the (Ahumada type) Selberg trace formula for a semiregular bipartite graph G. Furthermore, we discuss the distribution on arguments of poles of zeta functions of semiregular bipartite graphs. As an application, we present two analogs of the semicircle law for the distribution of eigenvalues of specified regular subgraphs of semiregular bipartite graphs.