TY  - JOUR
ID  - Cho2017
LB  - Cho2017
AU  - Cho, Ilwoo
TI  - Non-factorizable C-valued functions induced by finite connected graphs
ST  - Non-factorizable C-valued functions induced by finite connected graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 2
SP  - 225
EP  - 263
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.2.225
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.2.225
AB  - In this paper, we study factorizability of \(\mathbb{C}\)-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) "non-factorizability" of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function.
KW  - directed graphs
KW  - graph groupoids
KW  - Redei zeta functions
KW  - graph zeta functions
KW  - non-factorizable graphs
KW  - gluing on graphs
SN  - 1232-9274
ER  -