The Signed Total Mixed Roman Domination Numbers of Graphs

Abstract The problem of signed domination of graphs is a typical optimization problem. It requires that each vertex and edge be assigned a feasible label so that the sum of assigned labels is minimized. First, we propose the concept of a signed total mixed Roman domination number and introduce the related research progress. Finally, we determine several lower bounds of the signed total mixed Roman domination numbers which depend on the parameters of vertex number and edge number, degree and leaf number.