scholarly journals A generalized Bartholdi zeta function for a regular covering of a bipartite graph

2013 ◽  
Vol 438 (3) ◽  
pp. 1025-1056 ◽  
Author(s):  
Iwao Sato ◽  
Seiken Saito
Keyword(s):  
Zeta Function ◽  
Bipartite Graph ◽  
Regular Covering

scholarly journals Weighted Zeta Functions of Graph Coverings

10.37236/1117 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Iwao Sato
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Equivalence Classes ◽  
Signed Graphs ◽  
Base Graph ◽  
Regular Covering ◽  
Decomposition Formula ◽  
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.

scholarly journals Bartholdi Zeta Functions for Hypergraphs

10.37236/1003 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Iwao SATO
Keyword(s):  
Zeta Function ◽  
Bipartite Graph ◽  
Zeta Functions ◽  
Selberg Zeta Function ◽  
Decomposition Formula

Recently, Storm defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of some regular hypergraph.

The Ihara zeta function of the complement of a semiregular bipartite graph

2021 ◽  
Vol 344 (12) ◽  
pp. 112598
Author(s):  
Deqiong Li ◽  
Yaoping Hou ◽  
Dijian Wang
Keyword(s):  
Zeta Function ◽  
Bipartite Graph ◽  
Ihara Zeta Function

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

Graceful Labeling for Some Complete Bipartite Graph

2018 ◽  
Vol 9 (12) ◽  
pp. 2147-2152
Author(s):  
V. Raju ◽  
M. Paruvatha vathana
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Graceful Labeling

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

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