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The coefficients of the reduced Bartholdi zeta function
- Publication Year :
- 2015
-
Abstract
- In this paper, we establish a new zeta function based on the Bartholdi zeta function for an undirected graph G called the reduced Bartholdi zeta function. We study the relation between its coefficients and the structure of the graph, and demonstrate that the coefficients count the star subgraphs in the symmetric digraph D ( G ) . Moreover, we investigate the properties of semi-principle minors extracted from the adjacency matrix of the oriented line graph of G . We also present a general formula for calculating all the coefficients of the reduced Bartholdi zeta function.
- Subjects :
- Mathematics::Number Theory
010103 numerical & computational mathematics
01 natural sciences
05C50 05C10 15A15
law.invention
Combinatorics
Arithmetic zeta function
symbols.namesake
law
Line graph
FOS: Mathematics
Discrete Mathematics and Combinatorics
Mathematics - Combinatorics
Adjacency matrix
0101 mathematics
Undirected graph
Prime zeta function
Mathematics
Discrete mathematics
Numerical Analysis
Algebra and Number Theory
010102 general mathematics
Digraph
Graph
Riemann zeta function
Computer Science::Multiagent Systems
symbols
Combinatorics (math.CO)
Geometry and Topology
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....dca6569edfd2f21d45e0eb4b31f22145