Abstract
A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. An edge-colored graph G is rainbow connected if every two distinct vertices are connected by a rainbow path. The rainbow connection numberrc(G) of G is the smallest number of colors that are needed in order to make G rainbow connected. In this paper, we study bounds of rainbow connection number of some graph operations, such as the union of two graphs, adding edges, deleting edges, and adding vertices and edges. Moreover, we also study the following extremal problem. Let k and n be two integers such that 1≤k≤ℓ<n. Find the smallest integer f(n,k,ℓ) such that for each graph G of order n and diameter k, there exists an edge set F⊆E(G¯) satisfying |F|≤f(n,k,ℓ) and rc(G+F)≤ℓ.
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.
