The Balaban index of a connected graph G is defined as J（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）DG（v）,and the Sum-Balaban index is defined as SJ（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）＋DG（v）,where...The Balaban index of a connected graph G is defined as J（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）DG（v）,and the Sum-Balaban index is defined as SJ（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）＋DG（v）,where DG（u） =∑w∈V（G）dG（u, w）, and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n vertices are characterized, respectively.展开更多
Balaban index and Sum-Balaban index were used in various quantitative structureproperty relationship and quantitative structure activity relationship studies. In this paper,the unicyclic graphs with the second largest...Balaban index and Sum-Balaban index were used in various quantitative structureproperty relationship and quantitative structure activity relationship studies. In this paper,the unicyclic graphs with the second largest Balaban index and the second largest SumBalaban index among all unicyclic graphs on n vertices are characterized, respectively.展开更多
Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying th...Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying the extremal graphs that exhibit the minimum or maximum Balaban index and sum-Balaban index within this class.Moreover,we provide a systematic ordering of all bicyclic connected chain graphs according to the magnitude of their Balaban index and sum-Balaban index.展开更多
基金Supported by the Natural Science Foundation of Anhui Province(1508085MC55)the Natural Science Foundation of Educational Government of Anhui Province(KJ2019A0817,KJ2013A076)+1 种基金the Project of Teaching Team of Chizhou University(2016XJXTD02)the Open Project of Anhui Universities(KF2019A01)
基金Supported by the Zhujiang Technology New Star Foundation of Guangzhou(Grant No.2011J2200090)Program on International Cooperation and Innovation,Department of Education,Guangdong Province(GrantNo.2012gjhz0007)
文摘The Balaban index of a connected graph G is defined as J（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）DG（v）,and the Sum-Balaban index is defined as SJ（G） =｜E（G）｜μ ＋ 1∑e=uv∈E（G）1√DG（u）＋DG（v）,where DG（u） =∑w∈V（G）dG（u, w）, and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n vertices are characterized, respectively.
基金Supported by the Natural Science Foundation of Anhui Province(Grant No.1508085MC55)the Natural Science Foundation of Educational Government of Anhui Province(Grant No.KJ2013A076)
文摘Balaban index and Sum-Balaban index were used in various quantitative structureproperty relationship and quantitative structure activity relationship studies. In this paper,the unicyclic graphs with the second largest Balaban index and the second largest SumBalaban index among all unicyclic graphs on n vertices are characterized, respectively.
文摘Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying the extremal graphs that exhibit the minimum or maximum Balaban index and sum-Balaban index within this class.Moreover,we provide a systematic ordering of all bicyclic connected chain graphs according to the magnitude of their Balaban index and sum-Balaban index.
