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.