TIGHT INDEPENDENT SET NEIGHBORHOOD UNION CONDITION FOR FRACTIONAL CRITICAL DELETED GRAPHS AND ID DELETED GRAPHS

The problem of data transmission in communication network can be transformed into the problem of fractional factor existing in graph theory. In recent years, the data transmission problem in the specific network conditions has received a great deal of attention, and it raises new demands to the corresponding mathematical model. Under this background, many advanced results are presented on fractional critical deleted graphs and fractional ID deleted graphs. In this paper, we determine that G is a fractional (g, f, n', m)-critical deleted graph if delta (G) >= b(2)(i-1)/a+n'+2m, n > (a+b)(i(a+b)+2m-2)+bn'/a, and vertical bar N-G (x(1)) boolean OR N-G (x(2)) boolean OR ... boolean OR N-G (x(i))vertical bar >= b(n+n')/a+b for any independent subset {x(1), x(2), ... , x(i)} of V (G). Furthermore, the independent set neighborhood union condition for a graph to be fractional ID-(g, f, m)-deleted is raised. Some examples will be manifested to show the sharpness of independent set neighborhood union conditions.