$$\mathbb {C}$$ C -Valued Functions Induced by Graphs

Non-factorizable C-valued functions induced by finite connected graphs

“…In Sections 3 and 4, we construct graph zeta functions, and review fundamental properties of such functions (also, see [6]). In Sections 5 and 6, we consider factorizability of graph zeta functions, and those of graphs.…”

“…But it is true that, under such conditions, we may lose lots of interesting analytic properties of graph zeta functions gotten from the pure algebraic-and-combinatorial properties of G (or of G). The following convergence condition (4.22) is obtained in [6]. then L G pv, sq is convergent absolutely, as an infinite series in C.…”

“…In [6], we attempted to connect the above two different topics, graph-groupoid theory and L-function theory, which seem completely un-related. For the graph groupoid G of a given graph G, we constructed a suitable order function , and then establish the corresponding Redei-zeta-function-like function…”

“…Analytic, combinatorial, and algebraic properties of tL G pv, squ vPV p p Gq have been studied in [6]. In [7], we showed that there exists certain inner structure…”

“…In [6], we established certain C-valued functions induced by directed graphs. Combinatorial properties of graphs was considered in terms of analytic tools from function theory, and vice versa.…”