|本期目录/Table of Contents|

[1]陈 语,陈海燕*.正则图联图的Ihara zeta函数及其应用[J].厦门大学学报(自然科学版),2019,58(01):83-86.[doi:10.6043/j.issn.0438-0479.201802013]
 CHEN Yu,CHEN Haiyan*.The Ihara zeta function of a join graph of regular graph and itsapplications[J].Journal of Xiamen University(Natural Science),2019,58(01):83-86.[doi:10.6043/j.issn.0438-0479.201802013]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
58卷
期数:
2019年01期
页码:
83-86
栏目:
研究论文
出版日期:
2019-01-24

文章信息/Info

Title:
The Ihara zeta function of a join graph of regular graph and itsapplications
文章编号:
0438-0479(2019)01-0083-04
作者:
陈 语陈海燕*
集美大学理学院,福建 厦门 361021
Author(s):
CHEN YuCHEN Haiyan*
School of Sciences,Jimei University,Xiamen 361021,China
关键词:
Ihara zeta函数 联图 基尔霍夫指标
Keywords:
Ihara zeta function join graph Kirchhoff index
分类号:
O 157.1
DOI:
10.6043/j.issn.0438-0479.201802013
文献标志码:
A
摘要:
G的Ihara zeta 函数是一个一元函数.首先用代数方法得到了两个正则图联图的Ihara zeta函数的一个因子乘积表达式,在此基础上得到了正则图联图的3种基尔霍夫指标(基尔霍夫指标、度和基尔霍夫指标和度乘基尔霍夫指标)之间的一个关系式.
Abstract:
The Ihara zeta function of graph G is a function with one variable.In this paper,by the algebraic method,we first obtain a factorial product expression of Ihara zeta function of join graph.Then based on the expression,we obtain a relationship among three Kirchhoff indices i.e.Kirchhoff index,additive degree-Kirchhoff index,and multiplicative degree-Kirchhoff index.

参考文献/References:

[1] IHARA Y.On discrete subgrouos of the two by two project linear group over p-adic fields[J].J Math Soc Japan,1966,18:219-235.
[2] BASS H.The Ihara-Selberg zeta function of a tree lattice[J].Internat J Math,1992(3):717-797.
[3] NORTHSHIELD S.A note on the zeta function of a graph[J].J Combin Theory Ser B,1998,74:408-410.
[4] SOMODI M.On the Ihara zeta function and resistance distance-based indices[J].Linear Algebra and Its Applications,2017,513:201-209.
[5] BAPAT R B,GUTMAN I,XIAO W.A simple method for computing resistance distance[J].Z Natur-Forsch,2003,58a:494-498.
[6] BONCHEV D,BALABAN A T,LIU X,et al.Molecular cyclicity and centricity of polycyclic graphs.Ⅰ.Cyclicity based on resistance distances or reciprocal distances[J].Int J Quantum Chem,1994,50(1):1-20.
[7] KLEIN D J,RANDIC M.Resistance distance[J].J Math Chem,1993,12:81-95.
[8] GUTMAN I,FENG L,YU G.Degree resistance distance of unicyclic graphs[J].Trans Combin,2012,1(2):27-40.
[9] PALACIOS J L.Resistance distance in graphs and random walks[J].Int J Quantum Chem,2001,81:29-33.
[10] PALACIOS J L.Upper and lower bounds for the additive degree-Kirchhoff index[J].MATCH Commun Math Comput Chem,2013,70:651-655.
[11] CHEN H,ZHANG F.Resistance distance and the normalized Laplacian spectrum[J].Discrete Appl Math,2007,155:654-661.
[12] GUTMAN I,MOHAR B.The quasi-Wiener and the Kirchhoff indices coincide[J].Chem Inf Comput Sci,1996,36(5):982-985.
[13] ZHANG F Z.The schur complement and its applications [M].Berlin:Springer,2005:1-13.
[14] CUI S Y,TIAN G X.The spectrum and the signless Laplacian spectrum of coronae[J].Linear Algebra Appl,2012,437:1692-1700.
[15] GUTMAN I.Selected properties of the Schultz molecular topological index[J].J Chem Inf Comput Sci,1994,34:1087-1089.
[16] KLEIN D J,MIHALI’C Z,PLAVSI’C D,et al.Molecular topological index:a relation with the Wiener index[J].J Chem Inf Comput Sci,1992,32:304-305.[1] IHARA Y.On discrete subgrouos of the two by two project linear group over p-adic fields[J].J Math Soc Japan,1966,18:219-235.
[2] BASS H.The Ihara-Selberg zeta function of a tree lattice[J].Internat J Math,1992(3):717-797.
[3] NORTHSHIELD S.A note on the zeta function of a graph[J].J Combin Theory Ser B,1998,74:408-410.
[4] SOMODI M.On the Ihara zeta function and resistance distance-based indices[J].Linear Algebra and Its Applications,2017,513:201-209.
[5] BAPAT R B,GUTMAN I,XIAO W.A simple method for computing resistance distance[J].Z Natur-Forsch,2003,58a:494-498.
[6] BONCHEV D,BALABAN A T,LIU X,et al.Molecular cyclicity and centricity of polycyclic graphs.Ⅰ.Cyclicity based on resistance distances or reciprocal distances[J].Int J Quantum Chem,1994,50(1):1-20.
[7] KLEIN D J,RANDIC M.Resistance distance[J].J Math Chem,1993,12:81-95.
[8] GUTMAN I,FENG L,YU G.Degree resistance distance of unicyclic graphs[J].Trans Combin,2012,1(2):27-40.
[9] PALACIOS J L.Resistance distance in graphs and random walks[J].Int J Quantum Chem,2001,81:29-33.
[10] PALACIOS J L.Upper and lower bounds for the additive degree-Kirchhoff index[J].MATCH Commun Math Comput Chem,2013,70:651-655.
[11] CHEN H,ZHANG F.Resistance distance and the normalized Laplacian spectrum[J].Discrete Appl Math,2007,155:654-661.
[12] GUTMAN I,MOHAR B.The quasi-Wiener and the Kirchhoff indices coincide[J].Chem Inf Comput Sci,1996,36(5):982-985.
[13] ZHANG F Z.The schur complement and its applications [M].Berlin:Springer,2005:1-13.
[14] CUI S Y,TIAN G X.The spectrum and the signless Laplacian spectrum of coronae[J].Linear Algebra Appl,2012,437:1692-1700.
[15] GUTMAN I.Selected properties of the Schultz molecular topological index[J].J Chem Inf Comput Sci,1994,34:1087-1089.
[16] KLEIN D J,MIHALI’C Z,PLAVSI’C D,et al.Molecular topological index:a relation with the Wiener index[J].J Chem Inf Comput Sci,1992,32:304-305.

备注/Memo

备注/Memo:
收稿日期:2018-02-18 录用日期:2018-11-28
基金项目:国家自然科学基金(11171134,11301217); 福建省自然科学基金(2015J01017,2013J01014)
*通信作者:chey5@jmu.edu.cn
更新日期/Last Update: 1900-01-01