Abstract
The intersection number of a digraph D is the minimum size of a set U, such that D is the intersection digraph of ordered pairs of subsets of U. The paper describes much of the work done in the area of intersection graphs and digraphs, and proves two main results: Theorem 1 The intersection number of the line digraph of D equals the number of vertices of D that are neither sources nor sinks. Theorem 2 If D contains no loops, the intersection numbers of total digraph, middle digraph and subdivision digraph of D are all equal to the number of vertices of D that are not sources, added to the number of vertices of D that are not sinks.
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.
