20.500.12556/RUP-22076 Totally regular mixed graphs constructed from the CD(n,q) graphs of Lazebnik, Ustimenko and Woldar Popolnoma regularni mešani grafi, konstruirani iz CD(n, q) grafov Lazebnika, Ustimenka in Woldarja The CD(n,q) graphs are connected components of q-regular graphs D(n,q) introduced in 1995 by Lazebnik and Ustimenko. They constitute the best universal family of regular graphs of prime power degree with regard to the Cage Problem which calls for determining the orders of the smallest k-regular graphs of girth g. The girths of the CD(n,q) graphs are known to be at least n+4 in case of even n, and n+5 for odd n. We propose to extend the use of the CD(n,q) graphs into the area of mixed graphs by adding directions to certain edges of the C(n,q)graphs. In the context of mixed graphs, graphs in which the number of incident non-oriented edges is the same for all vertices, and the numbers of out-going and in-going edges are also equal and the same for all vertices, are of special interest and are called totally regular mixed graphs. In view of the special properties of the original C(n,q) graphs with regard to cages, we believe that the totally regular mixed graphs we propose to study may also prove to be extremal with regard to properties sought for in the area of mixed graphs. cage problem girth degree mixed graphs problem kletk ožina red mešani grafi true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 12:26:09 2025-11-03 12:26:09 2025-11-18 03:05:39 0000-00-00 00:00:00 2025 0 0 12 str. no. 3, [article no.] P3.03 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-05-19 519.17 2590-9770 10.26493/2590-9770.1758.c16 ADAM_Jajcayova_Tatiana_2025.pdf ADAM_Jajcayova_Tatiana_2025.pdf 1 E433B15ED1534EDD34DE6E1960B614DF 554daf383d1b4e11efa5ad8a6434e7008d0888e9190beee2f9b42106b3a60811 9c4a90e4-b8a8-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32021 Založba Univerze na Primorskem 0 0 0