Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423712 | Electronic Notes in Discrete Mathematics | 2016 | 6 Pages |
Abstract
A mixed graph is said to be dense, if its order is close to the Moore bound and it is optimal if there is not a mixed graph with the same parameters and bigger order. We give a construction that provides dense mixed graphs of undirected degree q, directed degree qâ12 and order 2q2, for q being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to 9q2â4q+34 the defect of these mixed graphs is (qâ22)2â14. In particular we obtain a known mixed Moore graph of order 18, undirected degree 3 and directed degree 1, called Bosák's graph and a new mixed graph of order 50, undirected degree 5 and directed degree 2, which is proved to be optimal.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
C. Araujo-Pardo, C. Balbuena, M. Miller, M. ŽdÃmalová,