TY - JFULL
AU - Sizhong Zhou and Hongxia Liu
PY - 2010/2/
TI - A Neighborhood Condition for Fractional k-deleted Graphs
T2 - International Journal of Mathematical and Computational Sciences
SP - 201
EP - 204
VL - 4
SN - 1307-6892
UR - https://publications.waset.org/pdf/4161
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 37, 2010
N2 - Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
ER -