Abstract
A graph G is called a fractional (g, f, m)-deleted graph if the resulting graph admits a fractional (g, f)-factor after m edges are removed. An important fact in the characterization of a discrete graph dynamical system is played by the independent sets, i.e., subsets of the vertex set of G in which any two of them are not adjacent because they reflect the sparsity and stability of the graph system in somehow. The neighborhoods union of independent sets characterizes the local density and local clustering characteristics of the graph system. In this paper, we study the relationship between characteristics of independent sets and fractional (g, f, m)-deleted graph systems. The main contributions cover two aspects: first, we present an independent set degree condition for a graph to be fractional (g, f, m)-deleted; later an independent set neighborhood union condition for fractional (g, f, m)-deleted graphs is determined. Furthermore, we show that the results obtained are the best in some sense.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
