Abstract
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if there exists a vertex v in D such that (x; v) and (y; v) are arcs of D. For any graph G, G together with sucien tly many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is dened to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and to characterize all graphs with given competition number k has been one of the important research problems in the study of competition graphs. The Johnson graph J(n; d) has the vertex set fvX j X 2 [n] d g, where [n]
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.