# Search results for: Xueliang Li

Discrete Mathematics > 2009 > 309 > 21 > 6322-6324

Discrete Applied Mathematics > 2009 > 157 > 15 > 3332-3335

Discrete Mathematics > 2009 > 309 > 21 > 6322-6324

The Randić index R(G) of a graph G is defined by R(G)=∑uv(d(u)d(v))−12, 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 R(G)≥k(n−k), where the equality holds if and only if G=Kk,n−k. In this short note we give a confirmative proof for...

Discrete Applied Mathematics > 2009 > 157 > 15 > 3332-3335

The Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. Aouchiche, Hansen and Zheng proposed the following conjecture: For any connected graph on n≥3 vertices with Randić index R and girth g, R+g≥n−3+2n−1+72andR⋅g≥3n−9+32n−1+32 with equalities if and only if G=Sn+. This paper is devoted to giving...