On the minimal ABC index of trees with leaves
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- 作者：Wenshui Lin ; Peixi Li ; Jianfeng Chen ; Chi Ma ; Yuan Zhang ; Dongzhan Zhang<sup> ; sup><sup>zdz@xmu.edu.cnsup>
- 关键词：Atom-bond connectivity index ; Extremal graphs ; Trees ; Pendent vertices
- 刊名：Discrete Applied Mathematics
- 出版年：2017
- 出版时间：30 January 2017
- 年：2017
- 卷：217
- 期：part_P3
- 页码：622-627
- 全文大小：424 K
- 卷排序：217
文摘
The atom-bond connectivity (ABC ) index of a graph G=(V,E)G=(V,E) is defined as ABC(G)=∑uv∈E[d(u)+d(v)−2]/d(u)d(v), where d(u)d(u) denotes the degree of vertex uu of GG. A tree with minimal ABC index among trees with kk leaves is said to be kk-optimal. In spite of a few attempts, the problem of characterizing kk-optimal trees remains open. In the present paper a contracting operation and a splitting operation of a certain graph GG that decrease ABC(G)ABC(G) are introduced. With the operations, a few features of kk-optimal trees are obtained, which bring us a step closer to the complete solution of the problem.