Complete solution to a conjecture on the Randić index of triangle-free graphs

详细信息    查看全文

• 作者：Xueliang Li ; Jianxi Liu
• 关键词：Randić ; index ; Conjecture ; Triangle-free graph
• 刊名：Discrete Mathematics
• 出版年：2009
• 出版时间：6 November 2009
• 年：2009
• 卷：309
• 期：21
• 页码：6322-6324
• 全文大小：234 K

文摘

The Randić index R(G) of a graph G is defined by , where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. A conjecture about the Randić index says that for any triangle-free graph G of order n with minimum degree δ≥k≥1, one has , where the equality holds if and only if G=K_k,n−k. In this short note we give a confirmative proof for the conjecture.