摘要
Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + n-2δ+1/((n-1)(n-3)) .
Let G be a connected graph with vertex set V（G）, order n = │V（G）│, minimum degree 6（G） and connectivity s（G）. The graph G is called maximally connected if κ（G） =δ（G）. Define the inverse degree of G with no isolated vertices as R（G） =∑v∈ν（G） 1/d（v）, where d（v） denotes the degree of the vertex v. We show that G is maximally connected ifR（C） 〈 1 ＋2/δ＋n-2δ＋1/（n-1）（n-3）.
基金
Supported by the Natural Science Foundation of Xinjiang University（XYl10102）
Sup- ported by the of NSFXJ（2010211A06）
