Abstract

The problem of data transmission in communication network can betransformed into the problem of fractional factor existing in graph theory. Inrecent years, the data transmission problem in the specificnetwork conditions has received a great deal of attention, and itraises new demands to the corresponding mathematical model. Underthis background, many advanced results are presented on fractionalcritical deleted graphs and fractional ID deleted graphs. In thispaper, we determine that $G$ is a fractional$ (g,f,n',m) $-critical deleted graph if$ δ(G)≥\frac{b^{2}(i-1)}{a}+n'+2m $, $ n>\frac{(a+b)(i(a+b)+2m-2)+bn'}{a} $, and \begin{document}$|N_{G}(x_{1})\cup N_{G}(x_{2})\cup···\cup N_{G}(x_{i})|≥\frac{b(n+n')}{a+b}$ \end{document} 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.

Full Text
Paper version not known

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 call

Disclaimer: 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.