Neighborhood Union Conditions for Fractional ID-Deleted Graph
Wei Dong Gao · Journal of Kunming University · 2012
A graph G is called a fractional ID-(g,f,m)-deleted graph,if delete any independent set from G,the resulting graph is still a fractional(g,f,m)-deleted graph.In this paper,we extend some results on neighborhood union conditions for fractional deleted graph to fractional ID-deleted graph.It is determined following two results:1)If graph G with order n satisfies n≥12k+6m-11,δ(G)≥n/3+k +m and NG(x)∪NG(y)≥(2n)/3 for any two non-adjacent vertices x,y in G,then G is a fractional ID-(k,m)-deleted graph;2)If δ(G) ≥(an)/(2a+b)+(b2(i-1))/a+2m,n((2a+b)[i(a+b)+2m-2])/a,and NG(x1)∪…∪NG(xi) ≥((a+b)n)/(2a+b),for any independent set {x1,…,xi} in V(G),then G is a fractional ID-(g,f,m)-deleted graph.