具有较大Randi指数的4圈图
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摘要
研究了4圈图的Randi指数,得到4圈图中取得较大Randi指数的图的必要结构特征,并以1个特殊4圈图的指数值为界,证明大多数4圈图的Randi指数均小于这一临界值,进而给出前9大Randi指数和相应的极图,扩充了已有结果.
The Randi indices of the tetracyclic graphs is studied,and the necessary structural features of the larger Randi indices are obtained. It has proved that the Randi indices of most tetracyclic graphs are less than that of a special tetracyclic graph of boundary value,and then show the first nine Randi indices and the corresponding pole diagram,which is the expansion of the existing results.
The Randi indices of the tetracyclic graphs is studied,and the necessary structural features of the larger Randi indices are obtained. It has proved that the Randi indices of most tetracyclic graphs are less than that of a special tetracyclic graph of boundary value,and then show the first nine Randi indices and the corresponding pole diagram,which is the expansion of the existing results.
引文
[1]陈锦松,郭晓峰.关于Randic'指数及图的直径[J].厦门大学学报:自然科学版,2009,8(4):467-469.
[2]邓汉元,夏建业,夏方礼.六边形系统的Randic'指数[J].湖南师范大学学报:自然科学版,2003,26(3):10-13.
[3]周后卿,周琪.关于两类分子图的Randic'指数的计算公式[J].邵阳学院学报:自然科学版,2011,8(4):13-15.
[4]Randi c'M.On characterization of molecular branching[J].Amer Chem Soc,1975,97(23):6609-6615.
[5]桂云.两类图的次小Randic'指数的研究[D].合肥:安徽大学,2010.
[6]詹丽丽,刘素勤.给定悬挂点的三圈图的零阶广义Randic'指数[J].重庆工商大学学报:自然科学版,2012,29(6):4-8.
[7]Du Zhibin,Zhou Bo.On Randic'indices of trees,unicyclic graphs,and bicyclic graphs[J].Int Quantum Chem,2011,111(12):2760-2770.
[8]Dehghan-Zadeh T,Ashrafi A R,Habibi N.Maximum and second maximum of Randic'index in the class of tricyclic graphs[J].Match Commun Math Comput Chem,2015,74(1):137-144.
[9]Dehghan-Zadeh T,Ashrafi A R,Habibi N.Tetracyclic graphs with extremal values of Randic'index[J].Bollettino Dellunione Matematica Italiana,2015,8(1):1-8.
[10]Li Xueliang,Shi Yongtang.A survey on the Randic'index[J].Match Communications in Mathematical and in Computer Chemistry,2008,59(1):9-47.
[11]Gao Jinwu,Lu Mei.On the Randic'index of unicyclic graphs[J].Match Communications in Mathematical and in Computer Chemistry,2005,53(2):377-384.
[12]Lu Mei,Liu Huiqing,Tian Feng.The connectivity index[J].Match,1998,51(51):149-154.
[13]徐俊明.图论及其应用[M].2版.合肥:中国科学技术大学出版社,2004.
[14]吕宁宁.关于某些图的广义零阶Randic'指数的界[D].合肥:安徽大学,2010.
[15]Bondy J A.Graph theory with applications[J].Journal of the Operational Research Society,1977,28(1):237-238.
[2]邓汉元,夏建业,夏方礼.六边形系统的Randic'指数[J].湖南师范大学学报:自然科学版,2003,26(3):10-13.
[3]周后卿,周琪.关于两类分子图的Randic'指数的计算公式[J].邵阳学院学报:自然科学版,2011,8(4):13-15.
[4]Randi c'M.On characterization of molecular branching[J].Amer Chem Soc,1975,97(23):6609-6615.
[5]桂云.两类图的次小Randic'指数的研究[D].合肥:安徽大学,2010.
[6]詹丽丽,刘素勤.给定悬挂点的三圈图的零阶广义Randic'指数[J].重庆工商大学学报:自然科学版,2012,29(6):4-8.
[7]Du Zhibin,Zhou Bo.On Randic'indices of trees,unicyclic graphs,and bicyclic graphs[J].Int Quantum Chem,2011,111(12):2760-2770.
[8]Dehghan-Zadeh T,Ashrafi A R,Habibi N.Maximum and second maximum of Randic'index in the class of tricyclic graphs[J].Match Commun Math Comput Chem,2015,74(1):137-144.
[9]Dehghan-Zadeh T,Ashrafi A R,Habibi N.Tetracyclic graphs with extremal values of Randic'index[J].Bollettino Dellunione Matematica Italiana,2015,8(1):1-8.
[10]Li Xueliang,Shi Yongtang.A survey on the Randic'index[J].Match Communications in Mathematical and in Computer Chemistry,2008,59(1):9-47.
[11]Gao Jinwu,Lu Mei.On the Randic'index of unicyclic graphs[J].Match Communications in Mathematical and in Computer Chemistry,2005,53(2):377-384.
[12]Lu Mei,Liu Huiqing,Tian Feng.The connectivity index[J].Match,1998,51(51):149-154.
[13]徐俊明.图论及其应用[M].2版.合肥:中国科学技术大学出版社,2004.
[14]吕宁宁.关于某些图的广义零阶Randic'指数的界[D].合肥:安徽大学,2010.
[15]Bondy J A.Graph theory with applications[J].Journal of the Operational Research Society,1977,28(1):237-238.