A NEIGHBOURHOOD CONDITION FOR GRAPHS TO BE FRACTIONAL (k, m)-DELETED GRAPHS
Sizhong Zhou · Glasgow Mathematical Journal · 2009
Abstract Let G be a connected graph of order n, and let k ≥ 2 and m ≥ 0 be two integers. In this paper, we show that G is a fractional (k, m)-deleted graph if $\delta(G)\,{\geq}\, k+m+\frac{(m+1)^{2}-1}{4k}$, $n\,{\geq}\, 9k-1-4\sqrt{2(k-1)^{2}+2}+2(2k+1)m$ and $|N_G(x)\cup N_G(y)|\,{\geq}\,\frac{1}{2}(n+k-2)$ for each pair of non-adjacent vertices x, y of G. This result is an extension of the previous result of Zhou [11].