Vertices x and y dominate a tournament T if for all vertices z 6 = x; y; either x beats z or y beats z. Let dom(T) be the graph on the vertices of T with edges between pairs of vertices that dominateâ€¦ (More)

A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e. a hamiltonian path. Given a tournament T , it is well known that itâ€¦ (More)

A set S âŠ† V of vertices in a graph G = (V, E) is called a dominating set if every vertex in V âˆ’ S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graphâ€¦ (More)

Let denote a permutation of the n vertices of a connected graph G. Define (G ) to be the number P |d(x,y ) d( (x ), (y ))|, where the sum is over all the n2 unordered pairs of distinct vertices of G.â€¦ (More)

Two new elementary proofs are given of Landau's Theorem on necessary and sufficient conditions for a sequence of integers to be the score sequence for some tournament. The first is related toâ€¦ (More)