Seminar on Graph Theory titled by "The d++- Range Problem in Oriented Graphs".
Author: Aya Alhussein
Location: Lebanese University - Faculty of Sciences, Department of Mathematics, KALMA Laboratory, Beirut
Time: 31 July 2026, at 9:30 AM
Abstract: Unlike the first out-degree, the summation of the second out-degrees of the vertices, denoted by d++(D), is not constant with respect to the number of vertices and arcs. In this context, we asked for the range of possible values of d++
(D) over all orientations D of a given undirected graph G, which we will call the d++-range of G, and answered it for complete graphs, by characterizing, as a function of some integer n, the values that can be the summation of the second out-degrees of the vertices in a tournament of order n. Also, we solved completely the problem for paths, cycles, and grid graphs. These results provide a foundation for further investigations of the d++-range problem in oriented graphs, where several open problems are introduced.
