Domination Graphs of Extended Rotational Tournaments: Chords and Cycles

Abstract

Only the rotational tournament \(U_n\) for odd \(n \geq 5\), has the cycle \(C_n\) as its domination graph. To include an internal chord in \(C_n\), it is necessary for one or more arcs to be added to \(U_n\), in order to create the extended tournament \(U_n^+\). From this, the domination graph of \(U_t\), \(dom(U_n^+)\), may be constructed where \(C_k\), \(3 \leq k \leq n\), is a subgraph of \(dom(U_n^+)\). This paper explores the characteristics of the arcs added to \(U_n\) that are required to create an internal chord in \(C_n\).