Abstract
In an improper coloring, an edge \(uv\) for which, \(c(u)=c(v)\) is called a <em>bad edge</em>. The notion of the <em>chromatic completion number</em> of a graph \(G\) denoted by \(\zeta(G),\) is the maximum number of edges over all chromatic colorings that can be added to \(G\) without adding a bad edge. We introduce the stability of a graph in respect of chromatic completion. We prove that the set of chromatic completion edges denoted by \(E_\chi(G),\) which corresponds to \(\zeta(G)\) is unique if and only if \(G\) is stable in respect of chromatic completion. After that, chromatic completion and stability regarding Johan coloring are discussed. The difficulty of studying chromatic completion of graph operations is shown by presenting results for two elementary graph operations.
Sign-in/Register to access full text options 
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.
