Sizhong Zhou and Hongxia Liu
A Neighborhood Condition for Fractional kdeleted Graphs
202 - 204
2010
4
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/4161
https://publications.waset.org/vol/37
World Academy of Science, Engineering and Technology
Abstract&ndash;Let k &ge; 3 be an integer, and let G be a graph of order n with n &ge; 9k 3 42(k 1)2 2. Then a spanning subgraph F of G is called a kfactor if dF (x) k for each x &isin; V (G). A fractional kfactor 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 kdeleted graph if there exists a fractional kfactor after deleting any edge of G. In this paper, it is proved that G is a fractional kdeleted graph if G satisfies &delta;(G) &ge; k 1 and NG(x) &cup; NG(y) &ge; 1 2 (n k 2) for each pair of nonadjacent vertices x, y of G.
Open Science Index 37, 2010