泛连通图定理和Ore_2条件

Theorem of Path Connected Graphs and Ore_2 Conditions

记 Ore2 =min{ d(y) +d(x) |x,y∈ V(G) ,d(x,y) =2 } ,本文得到 :若 n阶图 G的 Ore2≥ n+1 ,则 G是 [5;n]泛连通图 .此是比 Faudree等人的定理进一步的结果 .

Let Ore 2= {d(y)+d(x)|x,y∈V(G), d(x,y)=2}. This paper shows that: If connected graph G of order n satisfies Ore 2≥ n+1, then G is Path connected graph. It is an improvement of Faudree schelp's theorem.