图的ABC指标与直径  

Atom-bond connectivity index and diameter of graphs

作　　者：武琳[1] 胡玉梅[1] 

机构地区：[1]天津大学理学院,天津300350

出　　处：《河北科技大学学报》2016年第6期552-555,共4页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11001196)

摘　　要：为了更好地研究拓扑指标在物理化学领域的良好性质,考虑基于度和基于距离的指标之间的关系问题,在直径这一作为距离的不变量的基础上,研究了图的ABC指标和直径的关系。根据相关引理,推导出了树和单圈图的ABC指标与直径的关系,得出了ABC指标和直径差值的紧的下界。For further study of the numerous nice properties of topological indices in physical and chemical fields, it is worth considering the relation between a degree-based index and a distance-based index. With the fact that diameter is an invariant based on distance, the relations between atom-bond connectivity index, diameter in trees and unicyclic graphs are studied. Based on relative lemma, the relation between atom-bond connectivity index and diameter in tree and unicyclic graphs is investi-gated, then the sharp lower bounds of the difference of index and diameter are given.

关 键 词：代数拓扑 ABC指标 直径 树 单圈图 极值 

分 类 号：O157[理学—数学]